What ages are the other children in your care?

A baby carrier is a great idea. Seems to me like the poor girl has some intense separation anxiety and needs some patience, love, and assurance. In addition to the carrier, maybe you could try setting a certain time each day to spend some quality, alone time this child? Preferably at the same time each day so she knows it's coming? Make the days as predictable as possible for her so that she can gain security from knowing what to expect. Be loving but consistent with her. You could try a variety of things to see what makes it easier on her, from filling the days up with fun activities, to the baby carrier, to alone time with her, etc. Be patient while trying different things and hopefully soon she will have adjusted to your home and she will be fine.

I agree that you need to be open and honest with the parents. Let them know that their daughter is having a hard time adjusting, so that if it's just not improving, you can let them know it's just not working and they won't feel like termination is coming "out of the blue."