Is there an effect that would allow you to force an opponent to cast a spell you own, without relying on cards from their library? A similar effect exists with Word of Command which forces them to cast a spell they own.
The only way I know to force an opponent to cast one of your spells without controlling their turn is Hive Mind, which reads
Whenever a player casts an instant or sorcery spell, each other player copies that spell. Each of those players may choose new targets for their copy.
They don't technically cast the spell, but they get a copy of it (and they don't get an option as to whether or not they get a copy - while they can control the targets, they can't choose to not play it like they could with Eye of the Storm. It won't increase their storm count, but they'll get the effect of the spell.
There's even a combo deck based around playing Hive Mind and then playing Pacts that your opponents aren't able to pay for, forcing them to lose the game.
There are a few ways to force an opponent to cast a spell you own. There are a number of permanent cards that allow you to cast cards from an opponent's library, including Chaos Wand, Daxos of Meletis, and Etali, Primal Storm. If you have a permanent like that, you can give it to your opponent with something like Donate or Zedruu the Greathearted, then take control of them with Mindslaver or Sorin Markov's ultimate and force them to use that ability. If you have some kind of deck manipulation too, you can choose which card they cast.
Alternatively you can cast the spell yourself, then transfer control of it to your opponent. To do this, you would use a Perplexing Chimera. As before, you can donate the Chimera to them, or just use the Chimera's own ability when they cast a spell, then control their turn and cast the chosen spell, and force them to gain control of the spell in exchange for the Chimera.
In most situations, these two options are practically the same: the player who controls the spell is the one who follows the instructions, and "you" on the spell refers to the controller. The primary difference is on-cast triggers. If a player has an effect that says "whenever you cast a spell" (like cards with Prowess) or the spell itself has "when you cast this spell" (like on Emrakul, the Aeons Torn), the triggered ability will be controlled by the player who cast the spell, not the player who controls the spell as it resolves.