Tyrion's less than stellar activities don't shine so badly on his family name and he can be quietly married off to a merchant's daughter or something. Joanna would probably also be more active in this regard.

Tyrion's whoring is a direct result of his traumatic experience with Tysha. And he loved Tysha because she was the only genuine person who showed him affection.

With Joanna in the picture, he would have been less likely to seek out approval from others (if we assume she'd not be like Tywin, but I highly doubt it). Once he's of age, I can imagine Joanna would look to form an alliance with some minor House, in a more honest and diplomatic way than Tywin did.

Remember, Tywin says he tried to get Tyrion a wife, but I can't imagine him being careful with his words or put a good word for the son that he hates so openly.