I would be encouraging play dates for her. Invite friends over to play or even stay the night. Let her build friendships away from the schoolyard and other interfering people

I agree that when it’s happening at school talk with the teacher about it.
I would also invite the mum and girl over and observe if you notice something and take this moment to share you concern in a caring way with the mum.

I would try to set up some play dates with this girl, ones where you’ll be there, maybe having a cuppa with the other mum. You may be able to sort out any issues this way

Straight to it. Maybe you and the other mum could set up,play dates with the 2 girls. Away from the school playground, they might learn to play together

Sometimes little ones are not aware that what they do and say is causing friends to not want to be friendly. Some things to consider:
Has your child behaved in a manner that might be causing a rift in her friendships? Does she tease or boast?
You may like to invite her friend to visit outside of school.
Is your little one in any out of school activities? Perhaps some of the other little ones have bonded in dance or a sport?
Let the mother know that this has not been resolved ( you are not responsible for her stress, however because of what is happening at home may be contributing to the behavior of her children ) and then speak to her teacher. If nothing changes go to the Principal, pull her out of school until the children who are set against her are dealt with. Volunteer to help out in the classroom, library or school tuck shop, your presence at the school may be enough to put a stop to the bullies.
Being bullied is not acceptable anywhere, any time. If necessary change schools.

I’d come straight out with it, no good leaving it till it gets worse & it’s not your problem if the other mum has dramas. She needs to do something. I would also ask the teachers what they think

If it is happening in the school yard I would go and speak with the teachers. They then can keep an eye on it in there time and also deal with it when it happens. And tell your daughter to go and tell the teacher if it is happening at school. This way you are not going to offend your friend as it will be a school matter.

How did you go with all of this?

I’d come straight to the point, don’t beat around the bush or say nothing because you think the other mum has too much on her plate, think of your dear daughter, she needs your help.

I’d talk to the other mum straight up. She mightn’t be aware and there’s no point beating around the bush.

Try talking to the mum as this needs to be sorted out, also try and see if this bully wants to come over for a play date, maybe it will help them get along. Do a talk at school in front of the class on how bullying affects others, maybe that will help this bully to stop their behaviour.

Children often have ways of sorting things out and change groups regularly; I would say leave it for now as it sounds as though the other mum has her plate full. A word to the teacher might help as she probably sees a lot of what goes on. Hopefully it’s just a phase that will pass.

Kids can be so cruel, I haven’t actually had to go through this yet but I think if (or when) it happens I’m going to be the mum who comes right out and says “this is not appropriate behaviour” nip it in the bud before it gets out of hand

Just come straight out with it, you need to find out what caused the rift. As 7 year olds are fickle and it could change again, you can’t blame the other child 100%, you have to go in wi an open mind,.

this is tricky, i think you have to talk the other mother in a friendly way.