Your mother may still file her taxes, but she is not required by IRS to do
so if earned income is below the IRS
minimum income requirement($10,400).
If you consider the $4000 as a gift to your mother, then you can exclude from child care credit. However, you are eligible to claim the credit if the amount was to compensate for caring for your child while you was at work.
See
the answer to the following FAQ regarding Child and Dependent Care Credit
qualifications.
https://ttlc.intuit.com/replies/3301418
