Definitely take her to the vet and have her checked out. You could also get a feliway diffuser or spray and/or use rescue remedy in her water bowl, to calm her a bit.
Most of all with this little one you are going to have to be patient. She will come out of her shell, it's just going to take time. Does she have her own safe room that she can retreat to if things get too much for her? If you can this would be a good idea. A room with a warm bed, her litter tray and her food (obviously not next to each other). The best way to get her used to you is to just sit in the room with her and talk in a quiet voice, or read a book out loud, to get her used to you being around. Make sure it is her that is approaching you, not the other way around, and always come down to her level. If she likes treats you can try enticing her with those, but don't push the point.
She's not a deadbeat, she's just been through a lot and hasn't had an ideal start to her short life. With love and care she will blossom but you have to be patient and try not to push her. She would be feeling overwhelmed and probably frightened at the moment, as a lot of kittens do when they leave their cat family.
When she's getting a bit more confident you can try playing with toys, ones on strings are best, so it keeps a bit of distance between you and her. If she's not interested then just leave it for another time. It's important that you teach the whole family all of this, including the kids, so that everyone is on the same page and doing the same thing. Explain that she's timid and that she will come out of her shell eventually.
http://www.caring-for-your-cat.co.uk/timid_cats.html There's some good info on here, have a read and put it into practise. Please don't give up on your little girl, I'm sure she will reward your persistence with many years of love and affection once she is comfortable with you all.