During your round, you must play all your people, one at a time, and you may also use one Special Action from the current face-up Special Action card. So you perform the following loop:
As long as you have people still in your house:
- Play a family member or
- Play your Special Action if you haven't played it yet
So you choose to play the Special Action instead of a playing a family member. In multi-player, this distinction is important, because if you take the Special Action, someone else could respond by taking a key resource or board Action that you also wanted. In solo play, this doesn't matter, because no one is going to deny you any space on the board.
Just to be clear, in neither the solo or multi-player rules do Special Actions stop you from subsequently using a family member. You can still play a Special Action, and use all your people. It's just that you can only do one at a time, and then each other player gets a go, where they may play a family member or Special Action, and so on. The rules on p.3 are quite clear:
There is a distinction between a Person Action and a Special Action. To take a Person Action, place one Person marker on the game board. Instead of taking a Person Action, a player can take a Special Action card and carry out at most one of the Special Actions that are described on it.
This player's Person markers remain in her home, to be used for additional Actions later in the Round.