Oh My! I'm reading this and you could be me! My situation was very similar to yours and here it is in a nut shell (I hope!) - if you search through my questions, I think I posted something similar... Myself and another mom are neighbors and have girls the same age (in K now). When we moved in I introduced myself to her 2x, gave her my numbers, she promised to call - nothing came from it. I ran into her again, she said I've been meaning to call - we have to get together (she didn't give me her number tho). Fast forward a couple years and our daughters are in the same K class. Now we see each other walking the girls to school and we start to talk, getting along pretty well. Then another mom moves into our little block and she and the other mom seem to click right away, and I'm clearly left out. Although, it's a bit different in that I never had a real connection in the first place - plus I'm funny when I meet new people - don't know why that is yet....
So they click and I'm feeling like you are feeling now, even the party thing (I got an "oh and you can come to" - because I was standing there - gee thanks). So I post on here and the best advise I got was to get off my block and start making new friends for my daughter and myself. So that's what I did. I asked my daughter who she liked to play with in school and we started inviting them over to play. She met a great girl who has become her BFF and I get along great with her mom.
Turns out my daugher doesn't get along well with the neighbor girl anyway (she's too bossy and pushy) so WE'VE had to distance ourselves from them. And as my daughter has made more friends, all of a sudden our friendship is more desirable....
I'd say, don't talk to them about it. I could not find a way in my head to talk to my "friends" about this without sounding desperate or paranoid or some other undesirable thing - 3 is just a funny number when it comes to women and friendships...
When you run into the other mom at the new school be polite, say hi, chat if it happens naturally, but focus your energy on other kids for your daughter to be friends with - don't be afraid to call moms you don't know and invite their kids (and them) over to play if your daughter shows interest. Rest assured, your daughter will make other friends, as will you.