You can claim any payments of services you made to your mother for watching your children. From you description, it's unclear whether you had any type of arrangement or made actual payments.
Helping with gas money or stocking your pantry while she stayed seems more like gifts. Additionally it doesn't sound like you have any receipts as proof of payment in the event of an audit.
Your mother would have to claim any payments as income on her tax return. The IRS will know if she doesn't because you have to put her social security number on your return in order to claim a credit.
Since she was not an employer, she would be considered self-employed and would have to pay self-employment tax in addition to income tax.
Payments to Relatives or Dependents
You can count work-related payments you make to relatives who aren't your dependents, even if they live in your home. However, don't count any amounts you pay to:
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A person for whom you (or your spouse if filing jointly) can claim as a dependent;
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Your child (including stepchild or foster child) who was under age 19 at the end of the year, even if he or she isn't your dependent;
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A person who was your spouse any time during the year; or
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The parent of your qualifying person if your qualifying person is your child and under age 13.
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