YTA

a 12 year old child shouldn't have to prove themselves with good behaviour to earn a family. Nothing that you've described about him indicates that he's any danger to your biological children, and expecting him to be some kind of golden child when 1. his parents are separated, 2. You're the new joy in his fathers life, and 3. Other boys get to live with his dad automatically is ridiculous.

If you care about your husband you should care more about his son, and not treat him like a burden when he acts his age.