Background
My wife and I recently moved into a town-house apartment in a large complex. We have a Husky pup that my wife walks twice a day (she's a stay-at-home) and the dog attracts lots of attention from the neighborhood kids. One of those kids is a 13-year-old girl (we'll call her "Angela") who has a rather unfortunate history. She's lost both her parents and now lives with her disabled grandparents who are, according to Angela, frequently ill and struggling with money. Angela herself appears to have many psychological issues that sound like, without getting too far into the reasoning, either bipolar disorder or borderline personality disorder. For what it's worth she's always very sweet to us.
The Setup
First off, my wife and I have no kids and no experience raising them, and we're in our late 20s, younger than any other apartment tenants in the community. Angela took a shine to our Husky and subsequently became friends with us. It started out just with her running outside to greet us when walking the dog, chatting for ten or fifteen minutes and then parting ways. When we found out her grandparents were sick and having trouble putting food on the table we even offered to make meals for her, which she always declines.
The Problem
Angela's comfort level with us has grown to the point where we find her knocking on or waiting outside our door multiple times a day to play with the dog, talk about friends, etc. to the point of being disruptive and actually ignoring her other friends. We've invited her in a couple times (with permission) to play games or watch movies, and tried to set expectations on only being available to do that on certain days/times, but still every day she's there waiting on the doorstep and one of us has to politely tell her we're busy and she has to come back another time.
With all that in mind, how can we make it clear to this girl she can't just show up any time and that she needs to spend most of her time with her friends? We like the fact that she feels she can open up to us about her problems and we want to help, but we know it's not healthy for her to start spending all her time with us instead of her friends, and we also can't sustain the amount of time she wants from us. My wife has tried to make it clear to her that just because she's home doesn't mean she's free to play, and she's also concerned other parents might start to think we're up to no good if Angela's other friends start telling them she's constantly ignoring them to hang out with us.
Update: For those interested, we've engaged directly with her guardians and learned a lot from them about her situation. She's actually getting psychiatric help (despite what she told us) and definitely seems to have some beginning symptoms of BPD due to childhood trauma/neglect. My wife has a strong desire to help, so we're trying to come up with a plan (with the guardians) to do so in a safe and constructive manner. As a side note, it's hard to pick a single "right" answer to this because the solution seems to be from parts and pieces of several of them, but I'll ponder it a bit further before accepting one. In the meantime further suggestions are always welcome. Thanks for everyone's input.