I don't know what Tyrion is thinking....
He should have planned with Jamie to be his champion
. That way, the situation would put Tywin and Cersei in a bad position. Tywin not wanting to lose his heir would have Cersei pick the worst champion in KL to fight Jamie so that he could win. That plan keeps Tyrion and Jamie alive. With Jamie as Tyrion's champion, Cersei would have never picked the Mountain...just my speculation...I don't know what that psycho would do but Tywin would keep her in check tho