Oh, yes, host something fun for your daughter and her friends, either a sleepover or just a neat time with a dvd, popcorn and whatever the girls want to do (within reason! :)).
It's good to teach our kids to let others do what they will, and to be concerned about making their own lives interesting in ways that are meaningful to them. Your conduct shows everyone what 'taking the high road' looks like, and this is a great example for your daughter and her friends.
It sounds as though this other mother/daughter pair are hard to read/easy to misinterpret, and you handled it well be redirecting the girls to focus on their own fun. If you keep up the habit of not taking these social slights personally, and just be positively responsive to this mother when she chooses to extend herself your way, you'll be modeling important skills for the girls. Everyone, in every walk of life, has to deal with people similar to this; sometimes, it's the girls at the office who got together after work but didn't think to invite you; or when in-laws or family do the same.
I can tell you from my own personal experience that some of these situations are not at all meant as a slight. However, if this woman is as hot/cold as you suggest, she's got her own problems and is likely modeling some confusing social practices for her child. And chances are, you and your daughter (and her friends) aren't the only ones to feel weird about this. Just think of all the girls who are going to this party... will some of them be invited the next time, or excluded? Sounds like a relief that your daughter is a bit outside this other girl's life and not within the direct sphere of influence, which would likely be even more confusing and mercurial.
Happy New Year's Eve to your crew. Wish my own mother had this sort of composure you are modeling. Pat yourself on the back there, Mama!
Best,
H.
PS-- If this other girl does say something untoward to your daughter or their friends, a polite but snappy comeback might be handy. "Oh, didn't your mother tell you that it's rude to discuss a party with people you didn't invite?" and walk away. Might let Little Miss Thing experience a bit of a reality check, maybe?