It's unclear - is your daughter also at private school, and these are her classmates who you feel are shunning her?
Or they are random local children? If yes, then where are your daughters classmates in this? Children are generally friends with the children they go to school with, not based on who lives near who.
We live in a village where average house price is around 700k, but children come in from cheaper surrounding areas, so my daughter (nearly 10, and 6) has a wide variety of friends at their excellent state school. We may count as the 'nouveau riche' you mention, having grown up in council houses but now living in a million pound plus house. In terms of playdates, I don't 'curate' them at all, beyond insisting that anyone she invites over treats her, me and our home with respect. Her best friends vary between a single mum who is a cleaner to a family who are multimillionaires. There is no 'discrimination' except on behaviours, and arguably that's setting healthy boundaries rather than judging.
We also socialise with some of the parents of her friends based on who we get on best with, and their children come along and all play together.
The only snobbery I have experienced is the inverse kind, those that call my daughter 'the posh kid', make negative comments based on her academic and sports abilities 'she is so annoying winning every race'. Which I appreciate is just jealousy, and I have tried to teach her to ignore it.