Usually it's something pretty obvious--prior abuse of the child, a sibling, or an adult partner, other criminal issues, drug or alcohol abuse, mental illness, or something similar with a current member of the parent's household (a teenage stepson who's a sex offender, or a girlfriend who has a family violence conviction, for example). Supervised visitation and child support do not have anything at all to do with each other. Her "filing for child support" probably just involves going through the AG, and that will not result in supervised visitation by itself--she'd have to file a suit in family court called a "SAPCR" and specifically ask the court for supervised visitation (and get you served, provide a good reason for requiring supervision, have a hearing, etc.) in order to get that.
First of all, visitation and child support are completely separate issues. I've seen many cases where supervised visitation was ordered for no other reason than lack of having legal representation.
You need to bit the bullet and retain an experienced family lawyer to navigate you through this maze.
Marc A. Pederson