Should I raise concerns with school about my daughter's treatment?

[BigBubblesX]

I'm not really sure what thread to use for this, and I've never encountered this before as this is my eldest child who is 4 years old. I'll give a bit of background, as I don't know what is relevant!
My DD started school nursery last May, the week after she turned 3. Another little girl started just over a week after her and she latched on to my DD instantly. Her mum stated that her daughter latches to people quite intensely and quite quickly. She was very clingy to my DD and wouldn't like her playing with other children etc. Last September they started morning nursery together, my DD would do half a day as I'm a SAHM so could pick her up but I wanted her to get used to being away from me for when she has to go to school. The other girl was in full days (8am until 5.30pm) as her mum works and is a solo parent (by choice as she had a donor because she couldn't be bothered with settling down [her words]).
Anyway, there were 2 occasions where this other little girl told my DD that she was the wrong skin colour and should be the same as her, my DD was quite upset on the second occasion and asked if changing skin colour is possible so she could be like her friend. I told her it isn't possible and she is perfect the way she is, and that she needs to tell the teacher straight away if this other girl ever says anything like this again (so we have a record of it). She didn't mention it again so I don't think the other girl said anything like that again.
During the school holidays she has asked for playdates with this other girl, and I have messaged the mother (we were friendly but I don't really like her views as she's incredibly racist!) And I never had any replies. On the last message I stated that I don't know if she wants to bother with is anymore so I thought I'd ask, her reply was 'I don't know how to respond to this.'
This September, as of last Thursday, my DD is in full time school (reception year) and has encountered nothing but issues with this kid! She is hitting and snatching from my DD constantly, and saying things like I hate you to my DD. This is upsetting my DD, I've told her it's clear that they don't want anything to do with us so maybe that's why the other girl is acting this way and that it is DD choice whether she wants to continue trying to be her friend or move on with other friends. My DD has said she wants to be her friend but doesn't like how she is being treated right now. I just don't know what to do, is this something I should raise with the teachers so they could potentially sit them down and find out what is going on? I would discuss with the mother but she is now ignoring me, like acting like a little bitch kind of thing, for example on Friday I was walking to pick up my DD from school and this woman's house is on the way, she opened her door and saw me, sort of stumbled around and stood there waiting for me to pass, then walked up the other side of the road completely ignoring me. Today she did the same, and then gave me an evil stare walking past me in the school yard. I didn't think mothers would be like this and I just don't know what to do. I didn't try to say anything as I'm actually quite pissed off and don't want to lose my cool with her so she thinks she's better than me!
I just don't know how to approach the situation with school really, should I speak to the teacher? As it's quite clear that I won't be able to solve this with the mother, I have raised an issue before when my DD came home with scratch marks from the other girl but she just claimed her DD wouldn't do that 🙄. It's fine if she doesn't want to be friends with me, I'm annoyed as I don't know what I've done to make her act this way with me but I don't think she's adult enough to have a conversation with me about it even after I asked her. I just don't want my DD to be coming home everyday upset by this other girl and the way she's treating her, we also have many years of school ahead so I'm dreading it. My DD has said she's hit her back today as the other girl kept following her when she walked away to keep hitting her, and I can't really blame her as she clearly has had enough and it's only day 3 of reception class 😕.
Sorry for the rambling, any advice would be appreciated

@BigBubblesX The bullly kid has told her mum that YOUR dd is being a bully towards her obviously or said something about her behaviour. I can not see any other reason the mum would act like this. Just tell your dd to stay away from her and talk to the teacher. Ignore the racist mum.

Of course you should speak to the school if this child is hurting your dd. It needs nipped in the bud, now.

If there are problems at school, eg behaviour of other children to your DC, then you speak to your child’s teacher. Do not get involved with the other parent. The school should be dealing with any issues that arise.
Your feelings about the mother are irrelevant, and you will look silly if you mention those to the teacher. Stick to what the child has done and how your DD has been affected.
Best to ignore any provocation and just say good morning cheerily as you pass by.

Definitely talk to the teacher OP and ask her to keep an eye on things. I don't think there's any chance of a productive conversation between you and the other mum given the history between you.

I just wanted to give back story, and having been told by society that you can't be racist towards white people, I assumed this is what I should have to do and put up with. I guess mumsnet mothers are just judgemental, thanks for that. Clearly an emotive topic for me.
I'll speak with the school as per the only poster who wanted to give advice. Have the day you all deserve

Ignore the mother. Speak to your child's teacher, it's unacceptable that your daughter is being hit or hurt. Tell your daughter she shouldn't be friends with someone who's nasty to her and encourage her to play with other children. Invite some other children for playdates.

Your thread got a bit taken over by someone without genuine intentions @BigBubblesX but to be fair your post is loaded with judgements, whether intended or otherwise it might be something to be aware of moving forward.

I would say it is always best to involve the teacher rather than the parent directly.

Thanks, I'll try and speak to the teacher tomorrow. I've suggested to DD that maybe it's best that she doesn't play with this other girl right now but my DD is upset as she wants to be her friend and doesn't understand why she is being this way, I have suggested maybe talking to her and asking her but it's not easy when they're 4. I'm not sure what the teacher will do, but maybe they just need to sit down together and find out what's going on? I'm not going to encourage this friendship outside of school, but I wanted things to be okay for her while she is in school and not coming home upset every day because her supposed friend is being cruel and hitting her. I've also explained that friends shouldn't treat her like this and should be fun to be around, but I think they've had lots of fun in the past so she is hanging on to that? It's quite a small school as well and I really don't want it to be awkward for her in class, but she isn't going to school to be spoken to like crap and hit so the other girl needs her behaviour addressed.
How should I act around the other girls mum? She's had such a horrid look in her eye towards me and I've just ignored her, should I continue to ignore her or just say hi? I'm not interested in friendship with her at all anymore, obviously with this behaviour, but I don't want a horrible atmosphere.

@BigBubblesX IGNORE the mum. She sounds unhinged to be honest so you dodged a bullet.