I would have a quiet word with the school. The mother clearly thinks her daughter can do no wrong and is unlikely to pull her up. If the teachers tackle the problem it will leave you and your daughter out if the loop, so to speak. Wisdom says you're going to be seeing a lot of both mother and daughter for some years, so best to be discreet about things. It does need tackling though. It may be fairly low key for now, but left unchecked...
My DD started at a new school a year ago September and this year has gone into Year 4. I have made one good new friend at the school, we both have DDs in Years 1 and 4 and I really like her and we have become quite good friends.
This week my DD1 has been coming home saying that friend's DD has been really mean to her. It sounds fairly low key - whispering, a few unkind comments, being a bit dismissive. My DD is quite sensitive to this kind of thing, compared to my DD2 who would most likely just go off and find someone else to play with and be quite matter of fact.
The other child has a reputation for this though and although we've never discussed it in relation to my child I get the impression the mother (my friend) is quite laissez fair and talks about it all being a normal part of the playground "stuff" that kids have to learn to deal with.
I am uncertain as to the best way to handle this.
1) Speak to school? 2) Speak to the mum - at risk to our friendship but obviously my priority is my daughter's happiness 3) Advise DD to ask the other child if she is intending to be a bully (my DDs idea) and then completely ignore