But you are causing "hard feelings" already. Oh, not on the part of some neighbors, but within your own sons.
You're telling them that you're willing to sacrifice your responsibilities around the home (laundry, dinners), and your attention to them, and the privacy of your own home, and your loyalty and fierce defense of your family, to a spoiled wandering neighbor child and her neglectful parents and grandparents. They're noticing.
She's not your foster child that you vowed to care for. She's not abused, apparently, and even if she were, you're not in a position, legally, to take her in. True, it's sad that her parents and grandparents have money but not love and time. But it's the parents and grandparents that are manipulating you, not the little girl. She apparently has not been taught rules, restrictions, boundaries and limits by her family. She's pretty young to manipulate, but the grandparents know how convenient you've made things for them!
Help your children learn the difficult lesson of standing up to do what's right, protecting one's family, making the home a welcoming place but one where rules are observed. Demonstrate kindness with boundaries by doing small things - when you bake yummy chocolate chip cookies for your sons, occasionally deliver a small plate to the girl for her to share with her grandparents. At her house. With no invitation attached. Speak kindly about their family and teach your sons the value of family, and teach them how important a parent's time and attention are (much more than money or travel). And defend your own home. Someday when your boys are older, you'll have to establish boundaries that often come with teen boys' friends (helping themselves to enormous quantities of food, rough-housing, objectionable language) and you'll have to say "we don't permit that in our home. You're welcome here, but we don't have open cans of soda in the front room near the grand piano" or whatever. And you'll have started that process now. It seems so innocent. A little girl, doing crafts. What's the harm, right? The harm is in the precedent you're setting, and the hard feelings are developing in your own children.
Please stand up for your family and speak up - firmly but politely. And don't just do it secretly. Tell your sons you were wrong to allow the girl to manipulate you, and tell them you appreciate their insight and tell them you love them. Tell them your home will be a welcoming place where they may bring friends, but there will always be limits and rules (no underage drinking, curfews respected, etc) and there will be food and fun and family and friends. Within reason.