回复：请问：上周四老大（4岁）在daycare被一女孩推倒后右手小指

If the accident happened on Thursday and nobody (including parents) thought it was a big deal till Sat., then I wound say the daycare did not do anything wrong by not taking him to hospital and etc.

As to medical expense, if the doctor thought it was caused by the accident, I think it is OK to ask the other parent to cover the cost that the insurance does not cover.