Can you deduct summer camp programs that my child attended while I worked during the summer

Yes, summer camp for your child while you were working is considered qualified expenses for purposes of the Child and Dependent Care Credit.

Yes if it is not an overnight camp and you meet the requirements. 

Why do overnight camps not count if parents were working during child attendance?

If both parents work at night or if a one parent family, that parent works at night, an overnight camp expense would be eligible for the child care credit.