As others have said, and from my own experience of a similar MIL, it won't be the meeting up that's the issue. It's the controlling way you go about it. There is no need to have set days to meet up, that makes it a duty rather than a pleasure and you'll find he meets you less and less because of this.
It's failing to respect that your son has his own life outside of your family group. You have to accept that if you meet up with him it will have to be at a time and place that works for you AND him and that will probably be without the 15 other people as thats just not feasible. He's a grown adult, he doesn't have to do everything on your terms anymore.
And stop blaming the girlfriend!!! I've taken the blame for this for 20 years. It's never been me, it's always been 100% her own son who finds his mum smothering, controlling and overwhelming.
He just says no to things, I try to tactfully explain the reasons why we aren't doing things (like your sons girlfriend seems to do) and suggest alternative things we could do. She blames me and double checks my 'excuses' as she is convinced I tell lies (i don't, theres no point anyway as she investigates everything i say!).
Final straw for me was about a year ago (20 years in!) when she accused me of one huge and quite ridiculous lie which made her and my FIL look really stupid and I realised she will never change. So I stopped trying and i stopped caring about them. I didnt shout or fall out but i just tell her to make arrangements for any meet up directly with her own son these days, i wont facilitate. The consequence is she's only had her grandchildren on her own for 2 hours in the last year. She now realises that the nasty wife was actually the one that kept re-building bridges and offering alternatives ways to meet up. She's pretty f**d on the meet ups and grandchildren stakes now as my husband won't make any effort.
I don't take any pleasure from this at all. I wish she would just meet us without the manipulation, control, expectations and demands for more and more. The mind games and bullying have caused my husband to have a breakdown. He's on antidepressants and sees a therapist weekly. I've struggled with sleepless nights and anxiety because of it too.
He tried to reach out to his dad and take him for a drink in a pub recently, just to try and keep that relationship going. She wouldn't allow it, insisted we ALL go (12 of us) and make it a big family gathering...he cancelled. It's sad, it's exhausting and it's all so unnecessary. If it wasn't like this we would meet weekly.