A couple of other things:
Dany's mother died from complications of giving birth. Jon's mother died from complications of giving birth. Tyrion's mother died from complications of giving birth. That could be something, how many other characters have their mothers demise drilled into out heads repeatedly over six seasons?
right, I already acknowledged that in the earlier post, re: a poster's earlier claim of using that connection as the "triple-headed dragon" in the prophecy or whatever it was. seems legit
There's also the way Tywin seems to accept Tyrion's whoring/drinking/insolence. Tywin was ALL about family. Since Jaime was Kingsguard and couldn't inherit, if Tyrion was a true heir who would have gotten Casterly Rock Tywin might have spent more time whipping him into shape.
Tywin was also a complete dick. While there may be something to that interpretation, it really isn't any more valid that just going with Tywin hated Tyrion and didn't really care about his boozing, never saw him as a legitimate heir, because he simply hated him for killing his wife...and being a freak. Besides, I recall Tywin already banging into Tyrion's head that he stood to inherit Casterly Rock, anyway, right?
Seems to me that Tywin was projecting most of his anger over how all of his children disappointed him in many ways: Jaime giving up his inheritance, Cersei being psycho, Jamie and Cersei constantly boinking and further proving the Lannister scandalous stereotypes--creating even more work for Tywin to bury their secrets--Tyrion being a boozing freak wife-killer. On top of that, Tywin knew that Tryion was the smartest and most capable of the bunch and that seemed to just piss him off more.
But this story is going into so many unbelievable connections, it's just as likely that Tyrion is the result of a past-traveling Bran-as-raven impregnating Tywin's wife in order to stir up descent among the Lannisters, poisoning their dealings for that entire generation.