It your child has the AP or EAD/AP combo card, he/she needs to go outside US (e.g. Mexico, Canada or Chinaa), then reenter US using the AP or EAD/AP combo card, thus his/her status will be Parolee (the passport will be stampped as parolee), not B-2, and then he/she can show the parolee stamp and I-94 to the school to register the school. If you need to go outside US with your child, you also need to have yoru approved AP.
Your child also can use the EAD to apply for SSN, and then apply for the health insurance any time.
