Are child care programs responsible for providing alternative eating utensils, larger spoons for instance, during mealtime for children with grasp delays? 

According to the Americans with Disabilities Act, “Centers have to make reasonable modifications to their policies and practices to integrate children, parents, and guardians with disabilities into their programs unless doing so would constitute a fundamental alteration.” So, yes, purchasing a few larger spoons can generally be carried out without much difficulty or expense to the program.