Yes. having a parent (child's grandparent) as day care provider does not disqualify you from claiming the credit. You still have to meet the other rules, such as you are working or going to school. Also, your dad cannot be your dependent. 

Your Dad will have to declare the income on his taxes, If he watches in your home, he may be exempt from the "nanny tax" (social security and medicare tax) because he is you parent*. If he watches in his home, he is subject to social security and medicare tax in the form of "self employment tax".

*If you are divorced or widowed, see "Exception for parents" at https://www.irs.gov/pub/irs-pdf/i1040sh.pdf