OP, you still haven’t answered whether your DH is refusing to do things with the younger DC on the weekends DSS is not there. I think this question is quite important in determining whether he’s overinvolved with DSS / uninvolved with the younger DC.
Aside from that - DSS may have a home and do fun things with his DM - but he only has one DF. Even if there’s a stepdad at his DM, he still only has one DF.
If he’s only seeing his DF eow and two nights a week, he will feel like he’s excluded from his DF daily life, because he is. He’s only there some of the time. There has to be quality to compensate for quantity. That doesn’t mean I advocate for ”disneyparenting”, it means that for your DH and DSS to be able to have a close relationship, your DH does have to put in a little bit of extra effort… not least to compensate for the fact that you clearly don’t want your DSS around. Perhaps if you were capable of treating DSS like he’s got every right to be there, this would not be the case.
Full disclosure - I grew up as a stepchild in between two homes (both parent remarried and had DC with their new partners). As others upthread have explained, this did not mean I had double everything, but rather I had two ”homes and families” where I clearly did NOT belong. I am not sure how to get you to understand why that is not ok, but unlike an adult who can ”start again”, a child can not go out and find new parents.
Now that I’m an adult, my Stepmother has tried talking to me about how difficult it was to have a Stepchild. How stressful it was to have me turn up eow (also meant DF was out of the house Friday after work and Sunday PM as he had to ”ferry me around”)… or, most recently, how she’d gathered up some pictures of me as ”they have limited wallspace” and ”obviously want pictures of their own children” on the walls. It was clear she genuinely thought I’d commiserate, now that I’m an adult. The thing is, I still don’t understand. I never will.
Threads like this are actually validating, because it really brings home that for all the stepchildren out there feeling excluded, less-than and unwanted there are step-parents genuinely feeling this is how it should be.
FWIW, OP - my stepmother was determined to exclude me from ”her” (and my DF’s…) family. I was never allowed to have time alone with my DF, as that would’ve been unfair. When I had DC, it became important to make sure they also didn’t feel included. She has chipped away, demanding less and less contact and I guess after 30+ years, my DF finally gave up. He hasn’t been to see me or my DC for years, but he has been very involved in his step-daughter’s (my step-mother’s DC from her previous marriage, who lived with my DF and her full-time) life and has very much been a loving, doting stepgrandparent to her children.
So - if you really want to push your stepson out of your lives, despite your DHs best efforts it might take you some years of grinding, but if you play your cards right, you can probably make it happen. I guess the question I’d be asking myself is, can you be sure (deep down) your DH won’t end up resenting you for it?