I think it's her party and she shouldn't be forced to invite someone she's not that friendly with and, in fact, doesn't like.
If you are having a party for just your daughter's friends, make it that. No neighbors, no other adults, no nothing. Just because you neighbors invited you doesn't mean you are committed forever for all future parties. Your daughter is an introvert and just wants something small with people her own age. When kids are 2 and 3, you just invite and plan the party. At 6 or 7, the child gets to plan. You can say "no" to 25 kids and a pony, but I don't think you need to pretend that there's a relationship between 2 kids of different ages just because they are neighbors and you like the parents.
Kids change their friendships all the time, and you don't need to invite everyone for the rest of her childhood and teen years just because there was a prior relationship. The kids have outgrown each other.
If you don't feel your older daughter needs her "own friend" at the party, and you want her to interact with her sister, then leave out the neighbor child. You don't need to make a big deal to the neighbor parents. It's okay to comment now and then that Janie is so introverted and is such a different personality than Susie is, it's hard to believe they come from the same gene pool, blah blah. You can even say (if you feel you should) that a big age range is too overwhelming for Janie so you are just having 4 kids from her class to keep it small and not stressful.
If you don't feel your older daughter needs to be there, then send her off on her own adventure, perhaps with the neighbor daughter. I wouldn't have her over as your older daughter's friend, as was suggested, just because your younger daughter doesn't like her. But that also sets a precedent for future parties so think about it.
Since your youngest didn't want to go to the girl's party last summer and you kind of made her do it, I think now's the time to let up on this. They don't like each other. Let it slip away! If there's a neighborhood BBQ, then they have to be polite. But this is your daughter's own birthday party and it should be HERS. You never know, the other girl and her parents may be relieved! They can't be blind to the lack of a strong friendship anyway.