AITA for not wanting my wife's other child

On mobile and all that, so sorry about that.

Ok, I'm in this dilemma. When I met my wife 10 years ago, she had a 1 year old. His real dad is a complete dumpster, never wanted to have anything to do with her or her son. I love them both, and I marry her a year later. Then we have another son, B, who is healthy and amazing. For three years, we're all happy. We were saving for a house, both working, and taking care of our two boys. Then we hit a rough patch. Money is tight, with daycare and neither of us had gone to college, but we're doing well, established in our respective industries. Then she starts to slip, spending time out of the house more, going out with friends. I'm ok with this, since she didn't have a traditional post high school life since she was pregnant her senior year of high school. But then she goes silent, and we rarely talk. Then on a Tuesday, she announces she's leaving. She grabbed some stuff and went to live with a dude she met at work, and had been seeing on the sly when I was home with the kids. Fast forward a few months, and she's back in town, her and her new BF have an apartment, and has more contact with our two sons. Then she gets pregnant with BF's kid, C. Fast forward another few years, and they all live with her and BF and I see my two boys on the weekend. Fast forward until last fall, they both get arrested, and DHS removed all kids, giving me full custody of my two sons, and placing the youngest with her sister. If her sister doesn't take him, he could be placed in foster care. Now I've spoken to my son's, and they both are kind indifferent to the youngest, C. C was treated like a prince, while A and B were both constantly ragged on by EX and BF. So the question, am I the asshole for not wanting to take in the youngest? He's not my son, and I've had very little contact with him.

(I've kept this very non descript because I don't want anyone I know to find out I'm reaching out)

EDIT- Thank you everyone for commenting. Maybe I can sleep a little (just a little) knowing I've tried my best. My boys are very important to me, and im going to continue supporting and loving them with everything ive got, and will be honest with them about everything. But someone's gotta get them up for school tomorrow, so good night to all you AITA folks.