Ahhhh my heart would hurt for my little girl, who is also 4, if she was in this situation. She is in a preschool that is for 3-6 yr olds and I see how much she looks up to the older 5 & 6 yr old girls. And they love her back, but they also do leave her out sometimes. It's the nature of their play. But you're talking of something different.
One thing that struck me is the subject of siblings, and since no one has mentioned this that I read, (I didn't read all of the responses), I thought I should mention it, cos I think it might have something to do with it. My 4 yr old daughter has a 3 yr old brother, and though I certainly don't recommend having children 13 months apart as we accidently did, they are as thick as thieves. Yes They fight alot, but that's because they are always playing together, and half the time each one has a different idea of how the play should go!
So my point is, your daughter might be especially drawn to your neighbours because she sees them playing together and this looks fun. My overall impression is that the mother and they must be a bit snooty, but on top of this, they have less need for playdates, cos the sisters have each other. It doesn't translate in my world, cos we still do tons of playdates, and I frequently have 1 or 2 extra kids in my house! But your Neighbour is not me and for some reason is not welcoming it. I cannot understand why. I do numerous trades with our multiple neighbours and that way I get some free time. Maybe she doesn't need this. Who knows. Anyway what I would do is to get active with setting up playdates with the friends she does have. Pay attention to the times that she is maybe most often bored and wanting to go see the neighbours, and arrange playdates with other friends at these times. I know it is so much nicer and easier to spontaneously call over the fence, rather than schedule something and drive across town. But it doesn't sound like your neighbours want to play. I would still ask when the opportunity arises, don't give up. Maybe more communication would help you understand why the mom is cold towards playdates. If you're feeling brave, you could just ask her why? I'm on the same page as my Neighbour friends, but maybe your parenting and lifestyle are not aligned with hers. Some people are very particular and no matter how hard u try, you're not going to fit into their tiny little box, which would probably be suffocating anyway. So focus your energy elsewhere if that's the case.