Can I stop paying child support if I’m not seeing my kids?

I’m under a child support order to pay my ex $600 every month for my 2 kids with her. She doesn’t like my new girlfriend and for the last 3 months hasn’t let me see my kids. I told her I’m not paying child support until she lets me see them like the visitation order says I should. She’s threatened to file contempt papers against me because she says her lawyer told her child support and visitation are two separate issues. Do I have to pay support if she’s withholding visitation from me? Can I file contempt on her for disobeying our visitation order and if I can, is it better to get a lawyer to do it?