I understand what you are saying BUT I have just had a biggish b'day party for DD at a local pub.
We worked on who we were inviting between us. Because it was in a pub I know some of the girls (and a boy) she is friendly with wouldn't be able to attend due to their religion. After checking with their parents that even if we had invited them they wouldn't be able to attend she invited the rest of the girls and boys in her class apart from one little girl.
This particular little girl has picked on my DD throughout the last school year to the point I have been into school twice, and I usually tell DD to resolve issues like that herself. DD is a lovely little girl, quite young for her age compared to some in her class and not as 'street smart' as some of them. So I usually take 'so and so was mean to me' etc etc with a pinch of salt as what DD feels is mean is usually just kids being kids.
On the friday before her party, little girls mother who wasn't invited asked me why (quite aggressivley) her DD hadn't been invited. I pointed out that others hadn't either, and that she wasnt a friend of DD's and that they didn't get on. This kids are now all 9 (my DD youngest in class) so quite able to say who they like and who they don't like. Other little girls mother accused me of being racist (her DD is mixed race) as there were 'only fucking white kids going' and me of being a 'stuck up bitch'.
I quite reasonably pointed out that her child had picked on DD for the last year and had been in trouble several times for bullying and that as I was paying for the party I could invite who DD wanted and didn't have to be dictated too. And that I could see where her DD got her attitude from. I'm also (visibly) 18 weeks PG and really didn't appreciate a foul mouthed fishwife screeching in my face on one of the hottest days of the year!
Now I am not saying that the OPs DD is anything like the girl we didn't invite BUT at the end of the day if you are paying for and hosting a party of any kind it is down to the host to decide who does and who doesn't get an invite. There may be issues between the DC's that no one is aware of and unfortunatly life sometimes is disappointing.
Confronting the mother won't achieve anything at all and as they are moving up to a new school I wouldn't dwell on it for a second. Kids are sometimes not picked for stuff or left out and the attitude that they should be invited to absolutly everything doesn't help them in the long run.