There's a lot for me to think about.
I believe that your choice to take time and think about it might mean that you're not a snob. I think a real snob is very selfish and doesn't consider others feelings- you are. You seem willing to let it play out and are trying to be flexible. Sounds like a good Mom to me. All this shows that you care about your children. Good thing.
In the end, if you've indeed made a mistake, that's you're right too. Everybody does, and then we learn how we might do differently next time.
I'm sort of going thru the same thing, I have a 9 and 12 year old and have not allowed them to play with other kids that in that kids backyards if their backyards are being used as pet toilets. I don't care if they clean it up eventually. If I'm wrong, I'm wrong, that family made a choice and I made mine. I'm willing to change my choice at a future date.