No, you can not claim your great grand child's daycare expenses unless you satisfy the following requirements.
Your great-grandchild is your dependent and a qualifying individual.
You paid expenses for the care of a qualifying individual to enable you (and your spouse, if filing a joint return) to work or actively look for work.
A qualifying individual for the child and dependent care credit is:
- Your dependent qualifying child who is under age 13 when the care is provided,
- Your spouse who is physically or mentally incapable of self-care and lived with you for more than half of the year, or
- An individual who is physically or mentally incapable of self-care, lived with you for more than half of the year, and either: (a) is your dependent; or (b) could have been your dependent except that he or she has gross income that equals or exceeds the gross income test amount, or files a joint return, or you (or your spouse, if filing jointly) could have been claimed as a dependent on another taxpayer's 2018 return.