Yes, you can count the money you paid your parent to claim the child care credit. You will have to provide the IRS your mother's SS#. Your mother may have to report the income, on her tax return.
Your next question might be: will this affect my mom's SS benefits. No. See https://www.fool.com/retirement/general/2016/05/16/can-you-work-while-receiving-social-security-disa...
How you mother treats the income, depends on where she works, your home or hers. If she works in her own home, her income is self employment and she will definitely have to file a tax return and pay self employment (social security & medicare - FICA) tax, if not actual income tax. If she works in your home, her income is household wages, and not subject to FICA, because she is your parent*. She will not have to file a tax return if the amount is less than $6350.
If your mother is your tax dependent, you are not allowed to claim the child care credit with what you paid her.
*If all of that wasn't complicated enough, your mother is subject to FICA if both of the following apply: (a) your child lives with you and is either under age 18 or has a physical or mental condition that requires the personal care of an adult for at least four continuous weeks in a calendar quarter, and (b) you are divorced and have not remarried, or you are a widow or widower, or you are married to and living with a person whose physical or mental condition prevents him or her from caring for your child for at least 4 continuous weeks in a calendar quarter.
