My ex-wife cheated and one of our two children isn't mine and I wish I had found out sooner or could be the bad guy and tell my child I don't want them to ever try to find their bio father

This is three years after finding out the truth. I was happily married (or so I thought) with two young kids when I found out my ex-wife was cheating. A DNA test showed our oldest was mine biologically but our youngest was not. I left my ex-wife and continued being the dad to my children. But I am bitter about the fact I will one day have to be okay with my child possibly wanting to know and have a relationship with their biological father. And knowing it's all my ex's fault makes me despise her more than I do for simply cheating. If I had found out way sooner I would never have taken responsibility for our youngest. But I love my youngest as much as my oldest. And then comes the part where I wish I could be the bad guy who tells my youngest I never want them to want any contact with their bio father. That's not fair to my child though so I have to be good, I have to come to terms with it and it's all my ex-wife's fault. I didn't sign up to be the non-bio. I didn't sign up for one day having to accept my child might want to know their genetic parent. I have been in therapy to work my way into acceptance. So I can be the good dad. But every time my ex-wife calls me just the stepdad or tells our youngest something about their bio father, I get so angry. She'll talk about him with our child without any heads up and then I get asked questions when our kids are back with me. One day I might end up sharing the title of dad. And it's something I will forever hate my ex-wife for.