If you paid for care in the provider's home, she is an independent contractor. She is responsible for her own income taxes, but to claim the expenses, you need her tax ID number. You need to download and give her a W-10 form that she fills out and returns to you. You include her tax number on your tax return to claim the credit.
https://www.irs.gov/pub/irs-pdf/fw10.pdf
If she refuses, you can try and claim the credit by writing "refused" in the space for the provider's tax number on form 2441, and include a written statement giving her name and address and that she refused to sign a form W-10.
If you paid for care that was provided in your home, then the caregiver is your household employee. You must get her social security number and issue her a W-2 for the wages you paid. You must also pay household employee's tax on your tax return.
