If your child is a direct threat to others, the center can refuse to serve you. For example, if your child bites other children, or runs out into the street if not watched, that might be a threat to safety. You might need a PCA to give your child the extra services to be safe.
If the day care staff changes the way they do things, sometimes the problem goes away. For example, they can change the schedule. Or if a certain game causes trouble, they can play a different game when your child is at daycare.
If the center has tried and cannot find any way to keep everyone safe, then it can turn you away.