LKM, you and your husband are your stepson's only hope for a semi normal childhood, never mind how messed up his brain could be as an adult if everything is his jw Mom's way. I know you do not want him to sit outside during birthdays, class parties, etc., feeling like an outcast. And never mind High School, which can be brutal as kids try to find their niche anyway!
When he is with you, your rules should apply. As long as you do not speak negatively of his Mom and her beliefs, she needs to respect this. You don't tell her he can't go out in service, to the KH or participate in anything related to the witnesses, do you? Fair is fair. The problem you could have is if you were to sign him up for team sports, if she has him during a scheduled game/practice, she obviously would not co-operate in getting him there, or letting you take him.
Please keep this precious child busy exploring what his interests are, what he is good at. Sports, music, art, theater? Hopefully you and your husband are doing thorough research so you can refute wt things his Mom is indoctrinating him with, especially when he says he can't do something because it would make Jehovah sad, or Jehovah does not like it. Nobody wants to make God mad, so you need to be able to disprove his belief. I believe that if you both stay calm, loving and positive, he will want to spend more time with you, especially if you do not speak negatively of his Mom, so he does not go into protect mode.
Do you get report cards and newsletters from the school so you are aware of the activities that are going on that Mom may not want him to be involved in? School is such a large part of a child's life, they need to feel like they fit in.
I hope you can all work this out amicably, for the little guy's sake. All the best to you and your husband.