If the provider refuses to give you their identifying information, you should report on Form 2441 whatever information you have (such as the name and address). Enter “See Attached Statement” in the columns calling for the information you don't have. Then attach a statement explaining that you requested the information from the care provider, but the provider didn't give you the information. Be sure to write your name and social security number on this statement. The statement will show that you used due diligence in trying to furnish the necessary information.

You will have to mail your return.

Tell the provider that she can get a free EIN on the IRS website to use instead of her SSN.

In any case, she must claim this money as income, regardless of whether you claim a deduction for it.