I never understood why Tyrion didn't trap his father, and Cersei, by insisting on Jamie as his Champion.
Never mind his gimpy hand. You think Tywin or Cersei would let The Mountain butcher his pride n joy ? Or Cersei her lover / children's father ?
Remember that this is a Cersei with a still alive Tommen and Marsella. Still not so unstable as to not give a fuck.
Tywin too would never risk it. He knew he could always manipulate Jamie to quit the Kingsguard and his vows of celibacy.
At the end of the day, it's Jamie and his seed he wants as the next Lord of Casterly Rock. Not the imp / possible rape product Tyrion.
All he had to do was convince Jamie (and himself) that Tywin would never follow through with it.
If he did, then keep Oberyn as backup.
^that sure would've been checkmate.