I encourage you to contact your local SSA and give you the accurate information than asking each of us about it.
EDIT ::: by the way your question, if you are eligible for SSDI and then if the disability determination service aka DDS is the one who make decision to see if you are disabled.Which youare already on SSDI. Then any kid who are under 18 that may be eligible under parent's ssdi because they are minors. However there will be a payee representative issue.
again, contact your local SSA by making an appointment real soon.