I don't see any reason why DCF would need to "report" him to the Housing Authority. I don't know if they even make such reports, as putting people into a homelessness situation does not help the child they are seeking to protect. If the Housing Authority does receive such info about its tenants, what it would have heard, at this point, would only have been your case, as yours is the only case pending - his is speculative at this point. Legal tenant or not, DCF in this matter has you living at that address, so any consequences with housing would flow from your case. But again, I am unaware of such sharing of information. Focus on getting yourself on track, working with DCF and meeting its requirements, so that you can find your own home and keep custody of your daughter. Good luck.
To questioners from West Virginia & New York: Although I am licensed to practice in your state, I practice on a day-to-day basis in Massachusetts. I answer questions in your state in areas of the law in which I practice, and in which I feel comfortable trying to offer you assistance based on my knowledge of specific statutes in your state and/or general principles applicable in all states. It is always best, however, to work with attorneys and court personnel in your own area to deal with specific problems and factual situations.