There is a right to administrative appeal of the denial of your card. You received written instructions for utilizing the appeal process along with your notice of denial. That administrative appeal process is your recourse. Unfortunately, you are not entitled to an attorney to be appointed at public expense, and you will need to retain your own counsel if you wish to use counsel.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.
If you expunge the conviction, the BSIS may still give you a hard time. You should be able to explain away your conduct, especially if it was expunged. Unfortunately, there is no real solution to the Child Support issue.
Seth Weinstein, Esq.
Practicing throughout Southern California
This reply should NOT be considered a legal opinion of your case / inquiry. At this time I do not have sufficient factual/legal documentation to give a complete answer to your question and there may be more to the issues you raised then I have set out in my brief reply.