It's a solid theory!Speculation/potential spoilers:
I think George RR Martin has several big twists and turns in the plot of ASOIAF. I've been thinking, Tywin Lannister hates his son Tyrion. He tells him that he is no son of his. Besides being a dwarf, why does Tywin hate Tyrion so much? Tyrion is brilliant. Yet, Tywin wants nothing more than to send Tyrion off to the wall, out of sight or dead. To be fair, Tywins wife did die giving birth to Tyrion so maybe that's it. I wonder though... I suspect there is more to it than we know.
Back story: When Tywin married his wife, Joanna, The Mad King (Aerys Targ) drunkenly referred to the first night tradition where lords or kings would be allowed to bed the bride. The Mad King was known for sleeping with lots of women and getting what he wanted. It isn't stated in the books whether or not Aerys actually slept with Tywins wife but it created tension between Areys and Tywin, to say the least. There was a LOT of tension between those two for multiple reasons.
Anyway, I wonder if Tywin suspects Tyrion of being the seed of The Mad king? What if he is? That would be a crazy twist. Tyrion is referenced as having Targ characteristics in the first book....a dark, purple eye, a streak of light blonde, almost white hair.
Just a theory.