You will need to file a Suit Affecting the Parent-Child Relationship (SAPCR) in Harris County, and set it for a hearing on Temporary Orders. At that hearing the Judge will decide who has custody ("Conservatorship"), how much time each of you will spend with your child ("Possession") and child support.
There are many factors that go into determining who is going to get custody of your son. I would have to know a lot more about your case before I could speculate on that. But certainly if he did commit family violence in January, that would hurt his case. Where your son spends most of his night (assuming you are separated) is important.
Just because you are standing up for your rights does not mean that things will get ugly, but they may. You should consult with a lawyer for more information.
This information is not legal advice and does not form an attorney-client relationship.
If you are a stay at home mom, then this should happen no problem. To get custody of a child that is four months from the mother, can be described as very difficult, provided the mother is not doing drugs and spends a fair amount of time with the child. You need to "lawyer up" and file a suit affecting parent child relationship first, then will give you leverage to shut him down now. Do not delay, it will only cost you more in the long run.