Some Godly advice needed

A question:

(Jamie speaking) No pics with this post. I hope that doesn't deter some of you from continuing. : )

There is this girl. She's 16. She's attended the little ministry we have for gypsy kids for years now, but she's always stood out to me. She's quiet, shy and respectful. I have heard her mother and aunt who she lives with are prostitutes. There was always a desire within me to reach out to her more than the two times a week we meet with the kids right now, but if other kids find out, they get really jealous and angry. Well, now that she's 16, she's been coming to church so after church one day, we brought her back to our house for a visit. It was really nice being able to have some one on one time with her and I felt alright knowing she's old enough now to visit our house with a reasonable excuse for the other kids since she's 3 years older than all the other girls. After the first visit, she came back the next day... and the next. One day I had in mind to just spend time with my girls, but guess who came over unexpectedly. She stayed for almost 4 hours. I have to practically kick her out every time. I think you get the picture. Now every time I see her, she asks when she can come over, and even on days when I've said I would be busy, she's showed up anyways. The thing is, we came here to minister to people like her. I've asked her if she has friends, she said yes, but I've never seen her with one and wonder if she did, why'd she spend so much time here? Knowing what I do about her home life, even from things she's expressed to me personally, I could see why she wouldn't want to be there. But where do I draw the line? Others have told me to limit my time with her so she would come once a week, but I don't think I can do that. This is the reason we came here, but it affects my whole family, not just me. My ability to cook, clean, spend time with them, and do other ministries. At the same time, how do turn her away, leaving her only to go back to her home where there is nothing to live for? An honest question. Please, feel free to comment. I will prayerfully consider every piece of advice!

Jamie