I think the problem isn’t baseball. The problem is that your wife and maybe you are still fighting but you are doing so through your son. If you were focused on your child instead of on who does what or differences in opinion about what is best for him, the two of you would be able to negotiate getting him to games and practices, regardless of who he is staying with at the time.
It won’t damage a child for life to not be allowed to play a particular sport. It can damage his relationships with both parents, his sense of himself, and his ability to trust and love if he is in the middle of his parents’ inability to co-parent in a way that is in his best interests, not their own.
I strongly urge you and your wife to involve a mediator or family therapist to help you figure out how to co-parent and get your son out of the middle. He deserves better. Both you and your wife will be better prepared for managing the many changes that go with parenting a teen.
I wish you well.