Can biological dad and I go in court, prove paternity and adjust birth certificate in Louisiana?

The father was on birth certificate because we were legally married but were separated. We are living in different states and only had one night together around conception. He sent me and DNA kit from out of state. He then reported that he was the father. I had no reason to think he would lie and claim a child that wasn't his. Years later, after never being able to produce the papers with one very believable excuse after another I stopped giving him the benefit of the doubt. He has now admitted it but he is the father as far as my child knows. I recently did a DNA test. The biological dad and myself want my son to know who he is but also not hurt my child by taking the 'father' he knows out his life. Well my ex doesn't want him to know at all and now wants to keep him at his house and making me take him to court to get my child back as he is on birth certificate as stated above. What are my rights? I want my son living with me and I will let him still visit his 'father' as I don't want to hurt my son because of my ex deception and selfishness. Does it have to be a lengthy process? Shouldn't we just be able to go in do DNA and case closed?