First step is to have another talk with your DH. Make the following points:
1) You're totally burned out on this girl, even though you know your DD loves her, so even though you're not saying no forever you are saying no for right now
2) You want to enforce a new dynamic where your DD has to ask every time she wants her friend to come over
3) Whichever parent says "yes" has to be in charge, because you're feeling like your DH is obligating you to watch the girls.
So the practical result of this would be to not have the girl over at all this weekend (to help you enjoy some time with your DD - can you guys come up with a family outing or something?). And in the future, if your DH says yes she can come over, HE is responsible for watching them, feeding them, telling the girl when it's time to go home, etc. If he can't or doesn't want to do that, he needs to direct your DD to ask you instead. And if you both say no, your DD will need to either play by herself or play at her friend's house instead.
That doesn't solve the spending-money-on-feeding-the-neighbor-kid question, but I suspect that would be less of an issue if the kid is around less. And once you get over your burnout (as it sounds like you will, since you do like the kid and so does your DD), you'll enjoy having her around a lot more than you do now.