How can my husband adopt our daughter?

My husband and I have been together since we were 17. We are now almost 23. We have been married for over one year and have two daughters. An 18 month old & a 7 year old. Unfortunately, our 7 year old is not biologically his. I had her when I was 15 by some jerk who hasn’t seen her in since she just turned 2, 5 years ago. And even then he had only seen her maybe 6 or 7 times in those 2 years. He’s in & out of jail & owes thousands and thousands in child support. He’s broke into gas stations (got caught once), been arrested for stealing property, car hopped, and does drugs. My sister was married to his brother for about 5 years and they have a son together the same age as my 7 year old daughter. They are divorced now but still co parent. So my sister kind of keeps up with what my daughters bio dad is up to. He’s currently in rehab for the third time after making a deal with the judge to get out of jail. He has told my sister before that he will never sign his rights over because he knows that’s what I want and he said one day my daughter will want to see him, which doesn’t make sense because it’s not like she can’t go find him one day when she’s 18 even if he’s signed his rights over. Anyway, I know every state and country is different. I live in the US in Kentucky. Has anyone had anything similar happen to them where the father refused to sign his rights but the judge ruled it anyway? I’m afraid that’s pretty much impossible but I just want what’s best for our daughter. If I were to die or something I worry she would somehow go to him or his family & she has no clue who they even are and they are not good or clean people. She only knows my husband as her daddy and his family are wonderful people.