Custody dispute (not married)

Location: Alabama. About a month ago, I found out my boyfriend of 13 years ago was cheating on me. This is not the first time. There were numerous Facebook and instagram incidents. There was also a time that he had an affair behind my back while telling the girl that I was a non existent lazy mom. He moved out to Colorado to be with that girl. This was a few years ago. We have a 10 year old daughter together. For the past almost 5 years, he has not worked. He broke his leg and never went back even after he healed. He took on the role of caretaker for our daughter. He would put her on and off the bus and help with homework. I paid all of the bills. I work at a specialty doctors office and sometimes have to stay late due to emergency patients. He eventually grew tired of his life and being bored all of the time. He puts everything on me. I will admit that I could have done more with him as a family. I should have played on my phone less. All of these things do not constitute cheating. He moved in with his long time friend and wants to see our daughter all the time. He lives about an hour away now. He wants me to agree to a custody agreement. I am not keeping him from his daughter. My issue is that he is showing pictures and telling our daughter about the new woman in his life. I absolutely do not want my child to meet her. What are my rights? I can prove that I have been financially responsible for her entire life. I take her to all appointments.i make sure that she has everything she needs. We are currently living with my mom and brother. They help take care of her throughout the day. I don’t trust him. He blames me for being angry and doing this to spite him. What would happen if we went to court? Are there ways to get a custody agreement outside of court? I also have documentation from years ago with him strangling me and throwing me into a glass door. I did not press charges because I was you and dumb, but it is still documented with the police. He has had a kidnapping charge against the girl in Colorado because they got into a fight and she locked him out. He was trying to get his dog, but things escalated. Should I go to court? What am I looking at paying? I know that he is currently looking for a job now.