How to legally step parrent adopt?

Hi, I have a question about step parent adoption. My ex boyfriend and I have never married we had a son who is two years old. We split up a year and three months ago. I am aware that in the state of Ohio, an unmarried woman who has a child has all rights unless said otherwise by a court. We have never went to court over custody because my sons father says he doesn't want too. My current fiance and I are getting ready to get married. He is enlisting in the military which means we will be having to move to a different state or even country after he is stationed. My fiance wants to legally adopt my son. My son's biological father picks and chooses when he wants to see or take his son. He's went months without seeing or even texting to ask how our son is. He always has as excuse every time I ask if would like to see our son or take him for the weekends. He ignores me a lot and doesn't work with me at all when it comes to our son. During the three months my sons father disappeared, I had our son just about potty trained. His father took him for a week and now my son wont use the bathroom at all! I know for sure he does drugs but have no way to prove it. and if he is told he'll have a drug test, he buys synthetic urine. He did it when he had to go to court for custody of his first daughter. OR he stops long enough to get clean and test clean then goes back. He doesn't support him in anyway. My fiance and I do. He is on child support for $183 a month, told the lady at the hearing he will work under the table so he doesn't have to pay. He has only made one payment of $93. He is trying to tell me that I am not leaving state with his son and my fiance is not adopting his son. He wants to have control of what i do with him but doesn't want no part in his life. How would I go about this to get my son adopted after we are married?