Can insurance co remove child from family policy if ill after the fact?

Generally, if the child became ill after the policy became effective and was a covered insured on the policy, then the insurance company should not be able to drop coverage. If the child became ill due to a pre-existing condition that was not disclosed at the time of the policy write up, it is usually considered fraudulant information and the child can be declined coverage. Again, this is not a definative answer. Laws vary state to state. Check with your state's department of insurance for an accurate answer.