I think it’s correct to say Tywin would have tolerated Tyrion to an extent, had Joanna survived. The point is, whereas lots of Tywin’s hate generates from Joanna’s death and the subsequent and misplaced blame for it, that’s not all of it. In fact, most of it is nothing but bigotry (extraordinarily common, in the westerosi mentality) about Tyrion’s condition, and mostly Tyrion’s condition seen and perceived as a punishment from the Gods. Mind you, I don’t think Tywin to be an extremely religious man, but I do think show!Cersei’s words about her father and his relationship with the Divine are pretty accurate: “He believes in the Gods, he just doesn’t like them very much.”

Back to the point, I don’t think his opinion of his youngest son would have been much different because: a) a dwarf is still an abomination in the eyes of the people of Westeros, and as such a terrible slight to a House as noble as House Lannister (and we just know how much Tywin cares about the perception of his own family); b) do not forget Tyrion was considered the Just Punishment for the man who had become too powerful (hence the whole premise above about Tywin and the Gods) and as such it was unlikely Tywin would ever really have anything but disdain for him.

But of course it goes without saying Joanna’s survival would have counted for something. I know most people like to headcanon Joanna as a kind woman who would be gentle to Tyrion and sway her husband to be so as well, but I’m wary of that theory. Suspicious, actually. Joanna was ruthless, had to be in order to be Tywin’s kindred spirit: sure, she may have been softer than her husband, but I doubt she would have been a paradigm of Good the way many people want to depict her. And I believe that’s the reason why I’m not sure she would have liked or loved Tyrion, but she surely might have at least protected him on principle, because what we know of her is she was a Strong Mother and would have protected him no matter what. But would Tyrion’s status have changed drastically? I don’t think so. Maybe he would have been a tad more sheltered, but far from respected or cherished.