There are no stepparents involved in our recently divorced family, but I browse this subreddit occasionally because it offers insight into the co-parenting dynamic, so take my advice with a grain of salt.
My ex got involved in a long-distance relationship just two months after he moved out, so I find myself somewhat in the position of biomom in your scenario. I'll share my story to see if it helps you view things from a different perspective.
The first thing that comes to mind is that after 23 years together, his family is my family, too. I developed relationships with them beyond them just being in-laws and it isn't realistic to think we'd abandon one another just because I'm no longer with my ex. I am still in frequent contact with my MIL, and she actually stayed with me the last time she was in town. We've spoken about vacationing together, just like we have for the past decades.
It almost seems like you are expecting your SO's family to unplug BM and plop you in her place, which isn't at all reasonable. Until they've spent significant amounts of time with you, they aren't going to develop a bond with you. Until that happens you aren't going to feel the connection BM has, and maybe you never will. You don't get to be part of their inner circle just because you are sleeping with their son.
And I have some very strong opinions on spending time with the child. I think my own ex has gone about this in entirely the wrong way, and following the timeline of your relationship it sounds like you guys did the same. What he has done was to go off and create an entirely new life with someone else right out of the gate, and then try to drag our two teens into his new life. The kids have described having dinner with him as "listening to an infomercial about how great his new life is." What should have happened, IMO, is that he put his time and effort into getting new routines established with the kids, then slowly, slowly, slowly introduce any new partners into his life with the kids, not the other way around.
And that is why I understand and approve of them arranging the kid's visits for when you are not around. If the kid only gets to spend every other weekend with his dad, why on earth would anyone expect him to share dad's time and attention with you? Dad's relationship with you is entirely separate from his relationship with his son. To the son you are an outsider and just because dad loves you wants to spend time with you doesn't mean he has to.
We worked through family therapy earlier in the year and the therapist had some advice about introducing new partners that probably won't go over big around here, mainly being that it has to go at the pace set by the child. The way it should happen is that dad's and your feelings are irrelevant to whether the child feels comfortable meeting you or spending time with you. It doesn't matter one bit how excited and eager you are to spend time with the son. Unfortunately, the distance between you has put you at a severe disadvantage. Were you to live closer, gradually increasing visits as the child's comfort level increases wouldn't be a problem, but instead you do is go from zero contact with the child to popping into town expecting to just insert yourself into their lives. To the kid you are an intruder and it is expected and age-appropriate that he wouldn't care to spend time with you.
In our case, it is my ex who (until recently) has arranged for her to visit during times he doesn't have the kids. They've been together since last September, but the first time meeting the kids was even suggested was when she was here June/July, but the kids refused. Expanding on my comments above about introducing her into his life with the kids, what dad did was cancel the plans he already had with the kids, then invite them along to spend the weekend with him and his girlfriend. As I said, exactly backwards from what he should have done. What he should have done, IMO, is to gently request that she be allowed to join them in their previously planned activities.
When she was here again in August, the kids stopped by dad's apartment to meet her for all of five minutes. They said she seemed nice enough but weren't interested in ever spending time with her again. She's gone now, no idea when she'll visit again, so who knows what'll happen down the road.
For my part, I don't have a problem with him being in a new relationship per se, but I do think he hasn't handled this particular relationship very well and that it has needlessly complicated our adjustment to life as a divorced family.
I will leave you with something resembling words of encouragement from my daughter's therapist: "If this relationship is around for the long haul, time is on your side." You don't need to rush things with the child, and in my experience, if you do it'll only make things worse.