Check with the IRS.
For anecdata, we have the same setup. My mom lives with us, watches our little while we are at work, and cleans our house. She gets free room and board. We have a separate account for groceries for the whole house hold, she has a debit card for it in her name to get whatever food she wants within the budget. We gift her a car stipend for gas and oil changes. We also gift her a monthly stipend for spending money.
We do not claim the tax credit. But the benefits of having our daughter cared for by someone who loves her, and never doing day care drop offs and pickups are well worth it!