I think you need to give your head a wobble.
You haven't said how old the kids are. I'd also like to ask an additional question - how old are you, OP?
I think you're confused about what you want. Your list of issues includes always having the kids in tow and that being draining, but you also don't like being left out of invitations with other mums? This doesn't make sense.
You also say that you are drained by having other people's kids around for a couple of hours - if that's the case, have you considered how drained the parents might be after having them 24/7? You're nonplussed that they can't meet in the evening, but maybe that's why - they're knackered.
How many friends do you have, OP? I've got about 6 good friends, lots more casual ones. If I met only my good friends, child free, once each every two months, that would only leave me one Saturday a month to actually spend with my child. And while you might think that's okay, what's happening with the child while I go off giving my friends their alloted child free time? Oh yeah she's with her father - so that only gives him one Saturday a month to himself. So it's only fair that he gets to spend it with his friends, right? So then when do we all spend time together as a family? Obviously this is a very simplistic example but it isn't as simple as you are assuming.
There is a lot of inability to see things from other perspectives on this thread - from both sides. OP seems to be unable to recognise that her friends might be exhausted, struggling with cost of living, struggling with mental health issues, stressed from work, or any number of things that might mean they can't meet up as much any more. Similarly all the talk of "mummy martyrs" is not helpful - if people want their lives to revolve around their children, then they can! Freedom to choose! Yay feminism!
Friendship is not an obligation. You see your friends as often as you want to. I personally would have zero time for someone giving me a hard time for not seeing them enough. If they decided not to see me at all any more because it's not enough, then fine! Make that choice. But don't guilt trip me for giving you what I'm currently able/willing to give.