I haven't had time to read all of the responses but my 22 years experience doing home childcare tells me this: you have trained her that if she cries hard enough and long enough you will come and pick her up. She just needs more adjustment time and time to bond with the provider. In time she will learn to trust that the provider will and can meet her needs also. You will always be her preferred choice though and she will never want you to leave. You might try sending along a blanket from home with home smells on it for awhile.

Good luck!