The story which you mentioned about your husband used to happen wid my mom and us also. My father never used to understand and accept his mistake instead he used to give us earfull. So we decided that rather than pin pointing stuff, it’s better if we neglect the mistake made by such person and we ourselves try to sort out the mess without saying anything to him. If you stop this he would not abuse you infornt of you children and thus there would be no tension.
Just be mature and let go his mistakes and as you mentioned he has not been a good husband. Let it be, be emotionally strong and concentrate on your kid. Think as if they are the only world you have and everything you have or do is for them.
Be positive. One day your husband will realise his mistakes. Take care of your child.