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Playing Tywin in the Clash of Kings Scenario after you beat Robb you should get an event about picking your heir, Jaime is one of the options. It might also trigger if you lose the war, I don't know.
 
Jamie ended up as my heir when i was playing as Tywin from "Roberts Rebellion", but that was due to some stuff i cant remember ( he got to become the commander of the kingsguard after the rebellion, then after another succesion war where Hoster Tully became king, he got kicked out of the kingsguard).
 
This was a few versions back, but I also played Tywin in the Robert's Rebellion scenario. I'm not sure if I sided with Robert or declared my own independence, but I went to war with the Targaryens and got an event where Jaime killed Aerys and left the Kingsguard to come back to me, which was pretty cool. I don't even think the event is Jaime-specific, it's just based on what Jamie did in canon and has a chance to happen whenever a Kingsguard knight has a conflict of interest.