For anyone posing the OP question, or a similar one, I highly recommend visiting the Wikicarpedia page covering rules for "The River" and "The River II":
https://wikicarpedia.com/car/River
The short answer is that it's entirely possible to play with the River II only, and I agree with Gregor Thomas' assessment that this is actually preferable to play than with the River (I) set only.
I have both The River (I) and River II, in a set using the old (original) tile artwork, not the new more colorful tile artwork. I combined the sets, throwing out the duplicate tiles, so my expanded River set has 18 tiles. But that of course is just my own house rule, entirely and completely unofficial.
A continuing problem with the Carcassonne series of games is that it's been through many editions, and unfortunately the publisher(s) have not been consistent from one edition to the next, particularly in the way the original German rules have been translated into English in the various editions. The various rules for different editions of The River and The River II are thoroughly covered in the Wikicarpedia page linked above.
A significant problem specific to the rules for The River (I and II) is the prohibition against "U-turns". The original rules simply stated that U-turns are not allowed. (Note that River tiles, other than the River Start and River End tiles, are either curved River tiles or "straight" River tiles -- "straight" here meaning the River enters and exits on opposite sides of the tile, even if it meanders in between.) This would have been fine, but then unfortunately there was a later "official clarification" that said only immediate U-turns are not allowed. In other words, the intended "clarification" said that the only thing prohibited was placing two River curve tiles directly adjacent to each other with both curves in the same direction, forming an "immediate U-turn".
There are two problems with this revised rule:
It still allows the River to curve back on itself in such a manner that it's impossible to complete the River and makes it impossible to use all the River tiles.
It creates the possibility of having two parallel sets of tiles with only a single tile gap between, which greatly restricts the placement of tiles in those gaps. (And in fact, the diagram shown in the official rules for the River (I) show just a restrictive placement.)
Regarding point #1 above, the publisher responded to this criticism by replying -- and I'm paraphrasing here -- ~"If players choose to play in a manner that makes it impossible to complete the game, then that's their own fault."~ Well, I don't at all agree. It's the fault of the game designer if the rules allow a "legal" play that makes it impossible to play the game as intended. It's poor game design, period.
Now, the purpose of both The River (I) and River II tile sets is to create an expanded starting area, much more spread out than the original game's single start tile. This allows the "board" (the placed tiles) to expand much more rapidly, and allows many more possibilities for immediate expansion beyond the start. In my opinion that makes it a more interesting game, altho to be fair I note one YouTube review recommends against using The River expansion, because (according to the reviewer) it gives what he thinks is an unfair advantage to certain players, because some of the River tiles have good obvious meeple (follower) placement, but many others don't. Well, to each his own.
But, back to the problem with the rules "clarification". A simple fix, and the one suggested on the Wikicarpedia page, is to not only prohibit the placement of two River turn tiles immediately adjacent in a manner that creates an "immediate U-turn", but also to prohibit the placement of three River curve tiles all curving in the same direction. Or to put it more simply: If two River curve tiles are placed both curving in the same direction, then the third River curve tile must be placed with the curve in the opposite direction.
However, as I noted above, that still leaves the problem of allowing two parallel rows of tiles with only a single tile gap between, making it difficult to place tiles in that gap.
So, I made up my own house rules to prevent problematic placement of River tiles. Let me make it very clear that these are just my own "house rules", and are not in any way official. But they have been play tested, and do work to remove most of the problems caused by the official rules.
My House Rules for The River (I):
Sort out the River tiles from the regular tiles. Note River tiles are all marked with reversed colors on the back, making them easy to sort out when face down (but beware the original Start tile is also marked that way).
Shuffle the remaining game tiles and place them aside in stacks, for play after the River phase of the game has ended.
From the River tiles, sort out the Source (or "Spring") tile, and the Lake tile which is used for the end of the River. Set these aside.
Shuffle the remaining River tiles face down, and place them in a stack.
Place the River Source tile in the middle of the play area, as the game's Start tile.
Each player in turn, starting with the first player, draws the top River tile from the stack, and places it. (Note placement of the Source tile is considered to be part of setup, and happens before the first player's turn.)
Each River tile must be placed so that it continues the River.
Followers (meeples) may be placed on River tiles which have features which can be claimed and scored according to normal rules. However, the River itself is not a feature which can be claimed or scored.
The River divides fields. (Strangely enough, this is not stipulated in the official rules!)
Each time a River curve tile is placed, the next River curve tile (whether or not it is adjacent to another curve tile) must curve in the opposite direction.
The player who places the last River tile -- the Lake tile -- is not allowed to place a follower on that tile. Instead, placement of the Lake tile marks the end of the River phase of the game -- which is an expanded starting phase -- and marks the transition to the main part of the game.
The player who placed the last River tile also then takes the game's original Start tile, rather than drawing a tile from the tile stacks, as part of the first turn in the main part of the game. (Technically this means that player takes two turns in a row, but keep in mind they were prohibited from placing a follower on the last River tile, so that was not actually a full turn.) For players using the common house rule that each player draws a "hand" of three tiles as part of starting the main part of the game, then the original Start tile becomes one of the three tiles in the first player's hand. In this case, that player is not required to play the Start tile first.
Play then proceeds using the game's normal rules (that is, whatever rules the group has chosen for play). Any tile, including the original Start tile (if used), may be placed adjacent to any River tile, following normal rules for tile placement.
Final note: Use of the game's original Start tile here is of course optional. Players may instead choose to remove that tile from play when using River tiles, as stated in the official rules.
My House Rules for The River (II):
Note: The purpose of using the River tiles (either The River (I) or The River II) is to spread out the starting area of the "board", creating more options for play as the game progresses. Keep that in mind when placing River tiles. The rules below are an attempt to codify that purpose into a set of rules which will ensure that happens, and to do so better than the official rules. When written out, the rules below appear rather lengthy, and a new player might find them off-putting. However, if it is understood that the purpose of most of the rules below is only to ensure the play area is spread out and ensure the River doesn't loop back onto itself, then hopefully it should all be pretty straightforward, or at least it should be after playing the game once or twice. (Credit where it's due: The suggestion for using the River fork tile as the game's Start tile came from the Wikicarpedia page linked above.)
Sort out the River tiles from the regular tiles. Note River tiles are all marked with reversed colors on the back, making them easy to sort out when face down (but beware the original Start tile is also marked that way).
Shuffle the remaining game tiles and place them aside in stacks, for play after the River phase of the game has ended.
From the River tiles, sort out the River fork tile, the Source (or "Spring") tile, and the two lake tiles: The lake on the city, and the lake on the volcano. Set aside these four tiles.
Shuffle the remaining River tiles face down, and form into two equal stacks of 4 tiles.
Take one stack of River tiles and reshuffle, adding in the two lake tiles. Set aside the Source (spring) tile; it will be used as the last River tile.
Form the just shuffled River tiles into a stack. Place the other stack of 4 River tiles on top, then slide the Source (spring) tile underneath, so that it becomes the bottom tile in the stack of River tiles.
Place the River fork tile in the middle of the play area, as the game's Start tile.
Each player in turn, starting with the first player, draws the top tile from the stack of River tiles, and places it. (Note placement of the River fork tile is considered to be part of setup, and happens before the first player's turn.)
Each River tile must be placed so that it continues the River.
Followers (meeples) may be placed on River tiles which have features which can be claimed and scored according to normal rules. However, the River itself is not a feature which can be claimed or scored.
The River divides fields. (Strangely enough, this is not stipulated in the official rules!)
Note the River Fork tile has three "branches". A player may place a River tile adjacent to any of those three branches, in any position or orientation so long as it continues (or ends) an unbroken River branch, except for restrictions on placement of River curve tiles as noted below.
On the River Fork tile, one of the three branches is "in the middle" of the other two branches. Let's call that branch the "middle branch". Only a straight River tile may be placed adjacent to the middle branch of the River Fork tile; a River curve tile may not be placed there. A "straight River tile" is defined as a tile showing a section of the River which enters and exits on opposite sides of the tile, even if it meanders in between.
The first drawn straight River tile must be placed adjacent to the middle fork on the River fork tile.
If a player wishes to place a River curve tile adjacent to the River Fork tile (but not adjacent to the middle branch), that curve in the River must be in the direction away from the middle branch. However, if a straight River tile is placed adjacent to any branch of the River Fork, then first curve in that branch may be in either direction. (But note rule #18 below.)
Each time a River curve tile is placed, the next River curve tile (whether or not it is adjacent to another curve tile) on that same branch must curve in the opposite direction.
No River tile may be placed in a manner that would force two branches of the River to join. (Rivers don't flow in a circle in the real world, and they shouldn't in Carcassonne either!)
No River tile may be placed in a manner which would make legal placement of further River tiles impossible. Furthermore -- and this must be a guideline rather than a strict rule -- players are strongly encouraged to avoid placing River tiles in a manner which restricts placement of further River tiles. (This might well call for some judgement on the part of the players. It's impossible to state exactly all conditions which might force a premature end to placement of River tiles, without pages of explanation and/or multiple diagrams.)
A Lake tile, when placed, ends (and completes) the branch of the River where it is placed. No more River tiles can be placed on a branch which has ended.
The last River tile to be played will be the Source (spring) tile, which completes the last remaining branch of the River. The player placing that tile is not allowed to place a follower on that tile. Instead, placement of that tile marks the end of the River phase of the game -- which is an expanded starting phase -- and marks the transition to the main part of the game.
The player who placed the last River tile also then takes the game's original Start tile, rather than drawing a tile from the tile stacks, as part of the first turn in the main part of the game. (Technically this means that player takes two turns in a row, but keep in mind they were prohibited from placing a follower on the last River tile, so that was not actually a full turn.) For players using the common house rule that each player draws a "hand" of three tiles as part of starting the main part of the game, then the original Start tile becomes one of the three tiles in the first player's hand. In this case, that player is not required to play the Start tile first.
Play then proceeds using the game's normal rules (that is, whatever rules the group has chosen for play). Any tile, including the original Start tile (if used), may be placed adjacent to any River tile, following normal rules for tile placement.
Final note: Use of the game's original Start tile here is of course optional. Players may instead choose to remove that tile from play when using River tiles, as stated in the official rules.
