I think your problem is very definitely this mum, rather than school gate friendships in general. I've had similar incidents with two of my DCs - in one case my child was the aggressor and in one the victim. In both cases, the school reported what had happened first, so we all knew the facts.
When my DC1 hit another child, I made a point of ringing the other mum to apologise and ask what I could do to help. Obviously I really, really didn't want to - I was mortified (and she was a lawyer, lol) - but it was clearly the right thing to do. We both managed our children's feelings and behaviour, and the episode receded into ancient history.
Likewise, when my DC2 was being bullied by a group of kids, once the school had contacted the parents of the bullies, the ringleaders' mum came up to me outside school and did the same thing - apologised, asked how she could help. And again, we sorted it out.
To me, this is normal, civilised behaviour. I was never very sociable at the gate and didn't think of these mums as close friends, but we just got on with doing the right thing. I think the problem here is that the mum doesn't accept her child can have done something wrong. It suits her to cast you as the shit stirring villain of the piece, but is very immature behaviour and as damaging for her child in the long run as it's upsetting for you now. If what's happening is getting back to you, then clearly other people aren't even falling for her hype either.
I don't think this woman is going to morph into a reasonable person, so my best advice is to steer clear and advise your DD to do the same with her DD. If your DD was too scared even to report being hit, I think she needs some resilience training too. Back in the day, the recommended book was Bullies, Bigmouths and So-Called Friends but perhaps there's something more up to date. Widen her circle of friends, including outside school and be glad that Alice is being encouraged to go on playdates with everyone else - no doubt they'll all know soon who the problem child and mum are! You've got a way to go, but take heart from how much bigger secondary is and how much easier it is for quieter kids to 'find their people' there in my experience.