I think it's really important to grasp that school is for the kids, not the adults. Keep the kid part, ditch the adult. My life improved measurably when I stopped joining in all the school gate stuff.
We also had all sorts of shenanigans like you describe, I had the added bonus that my DD went to nursery with the ringleader's DD so she'd decided years before school started that she hated me for no apparent reason.
These days I drop off, I pick up, I exchange small talk, I go home and I put my energy into the relationships I know are worth it. My DD still has play dates with her friends (at theirs and at ours), I do the odd favour for mums of her best friends, they do the odd favour for me, but the important bit is that i don't let it infringe on my wellbeing.
I see it very much like work - I'm there to do my job and get paid, not to make friends. If I do make a genuine friend, it's a complete bonus. Working at the same place is not enough to base a real friendship on. Same at the school - I go there because I have to take my DD there.
I do have school mum friends, but I've known them for years now since our kids were tiny.
I'm actually very good at making friends as well, but I can't be doing with all that high school style nonsense!