You cannot claim the child care credit on your taxes without affecting mom's income tax.
If you claim the credit, she will have to claim the income. It will not reduce her SS payments, since she is at full retirement age.
If she has no other income, she may not owe any tax. That depends on whether she sat in your house or hers. If she babysat in your home, she is a household employee. Because she is your parent, she is exempt from paying social security and medicare tax, as a household employee.
If she sat in her house, she is considered self employed and must pay social security and medicare tax in the form of self employment tax
