actually, I can tell you a story from IBFD, to give you an idea of what to do:

I had made an alliance with Sassan (as and Arab), and also with the ERE. they were neutral to one another at the time. then one turn, certain "accidents" happened to the ERE and sassanids, causing the sassanids to attack the ERE. this meant I had the menu bar pop up asking which side must I take: I took Sassan's side.

another, fromEB:

I was waging war gainst the Carthaginians. they were allied to the Aedui, and both were truly annoying. so I went and made an alliance with the Gauls (Aedui), after trucing with them. their alliance to me cancelled the war with me and Carthage for one turn. then I attacked carthage, and since i was very generous to the Aedui, they went on my side: now 2 allies are enemies

the trick is to make an alliance (or at least a truce), with both, than attack one of them, while pampering the other. the pampered one will love you (the AI seems to bow down to my every diplomatic whim), and they will turn on the other ally, achieving your objectives. isn't that charming

another way is to frame the enemy factions, by making secret deals (the "accidents"), but that is trickier.

and no, I didn't use Force diplomacy...