I am not sure I follow this note - I think you are, in the beginning, talking about 2 different women. If I understand you, here are my thoughts:
Mom #1 may simply not check her email. I have one Mom friend who checks hers about 3x/year and then is too embarassed to respond to invitations that she received months earlier (and the dates have passed).
Mom #2 (neighbor) may not dislike you. Unless you see that she is REALLY different with other people than you, she may just not be outgoing.
My husband is a SAHD and he almost NEVER makes playdates for the kids. It doesn't matter how much he likes somebody, he just doesn't do it. The kids DO get to go on playdates and I am SO grateful for the 2 Moms who don't mind initiating almost every one of them!
Just like in HS, what other people think and do is rarely about us - it's about them. And even when it IS about us, it's still about them.