Tywin siding with the rebels made sense even without all that conspiracy stuff. The Targs heir was dead, their army beaten up badly and a hostile force gaining steam against them. Maybe the Lannister army turns the tide, but definitely not for sure. So Tywin had the option of join the rebels and for sure win the war and get a ton of rewards, or fight for a mad man who was clearly insane and unreliable and might not have rewarded his loyalty at all even if they do win, which wasn't even for sure.
It made way more sense for him to join the rebels, you don't need any kind of conspiracy theory for his motivation to make sense.
Tyrion being a secret targ would dramatically change his character arc and everything he has done and alot of the relationships he has had, and it would be completely out of left field and pretty stupid since we are just about 99% for sure going to get
as a secret targ. How many secret targs are there? it just gets dumb after a point.