Child support and health insurance

I was paying child support till the ex brought me to child support enforcement for more. I lost my job and she allowed me to see my son the time I wanted to see him. Between being able to see me son more and losing my job, child support enforcement said they had no case so everything was dropped against me. She has been my ex for a while now and in the separation agreement it states we have joint custody.
I recently got remarried and my wife has insurance. I told my ex that he can be added to our insurance and she refused cause it’s “HER” the new wifes insurance. The ex has had him on medicaid even before I lost my job. I guess its used to pay the copay for her. Now it pays everything.
Is she allowed to refuse insurance on my son because it would be through my new wife? I’ve had my son more than my ex does for a while now but she won’t agree to it cause she demands that my son lives with her and only her. She wants it to be known that he only “visits” with me.
I’m sure all this is leading to me taking her to court to establish court ordered custody but I know things will get ugly.

No, you may obtain insurance on your child.

If she tells me not to add him, can’t she use that against me later down the road? Saying that I didn’t insure him so she had to have him on medicaid which looks bad on my part.

I suggest you document your offers to insure the child.