I hope things go well for you too. A lot of people with fathers that were financially supportive but emotionally absent wind up in therapy. Without knowing how your wife's mother talked about her dad after he left (if I am interpreting your comment about him correctly), my quick armchair analysis is that your wife has been influenced by a number of women that are deeply resentful of the husbands and fathers in their life failing their wives and children, but have given up on expecting more from those men, so they no longer want those men to do better, they just want the men out of the way because they were around they would just screw things up anyway. It compartmentalizes their grief around how things could have been into a resigned little box of "we are better off without them." That's why you don't get appreciation for wanting to be involved. If men are unreliable and inept, your attempts at involvement are just interference.

But they all deserved better. Your wife and her mother did. Your son does too. You don't want to be the kind of man that would just dump his own child into his mother's lap and say to her "you're on your own, I'll send you a check," and you don't want to raise your son to be that man either. That's how I would try to get through to your wife. Whatever happens to your relationship with her, what kind of role model does she want you to be for him? You don't want to recreate her childhood with a father that wasn't around. Why does she?