He is repelling while at the same time craving to be loved, disciplined and cared for.
Mom needs to dote a little on him too, as there may be some jealousy not to be mentioned, but still going on. Mom may even resent men and he is feeling it. Whatever it is this child needs to be accepted for who he is, not what you want him to be. Right now he may not care about anything, including school---so give him something to care about.................
Find something to meet on common ground with----does he like animals, cars, sports, etc. Recognize that just now he is a boy stuck in a female world and may be in need of good MALE role model---possibly an after school soccer coach, YMCA, Rec center, Big Brothers---etc.
I wouldn't approach him about this, Instead I would find him a decent Male role model---to look up too, talk too about boy stuff,---boy stuff.
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Also remember that to this child (I do not know how long mom and your son have been dating) may not see you as family yet.
Also MOM needs to realize that just because he is now 12 does not mean that he is grown up, he needs her just as much as the baby does, and if he has been neglected due to moms doting on the baby----his current actions are the result of such. ( EX. "she doesn't care so why should I")
He is reacting to his situation which sounds a bit confusing for a 12 year old. Focus on the positive on the good he does rather than always focus on his negatives!