stepparent adoption or second parent adoption?

OK. So here is my situation. I have a 6 year old autistic son. His Bio dad didn't want to meet him until he was three and they have only seen each other in person like 6-7 times total. We live in seperate states and he doesn't even come to visit "our" son. He has tried to get out of child support since my son was 1. We have been going through court to establish parenting time, but he hasn't followed through at all. He now wants my husband to adopt, but that's where the problem is... my husband and I have only been common law married for about 6 months and my husband has a criminal record. He has nothing that would straight out prevent him from being able to adopt, but it would really depend on the judge so it's a risk.... so a lawyer brought up to me the idea of a second parent adoption. She said that it was intended for same sex couples, but really anyone who has a substantial part in my son's life should be able to be the second parent adoptee. My dad is willing to do it, if he can't, my mom will. Can that really work? My son's Bio dad is only giving me to the end of April to file a motion or he is going to try to get parenting time and take my son out of state.