I used to work in Child Support- an 'enforcement officer'.- main goal was to obtain & enforce support orders, especially for folks on public assistance.

Anyway- your court order will remain tied to the original court- if you divorced & neogotiated the settlement, including custody & support, in your home county, that county retains jurisdiction. He's partly right, the support & visitation can be reevaluated every 3 (at least down here) years. You can also petition the court for a review - especially of the support if there has been a dramatic change in your circumstances- like if he got a new job making a LOT more money.

He can threaten not to pay CS, but it's illegal. If you can't get any help
enforcing the the support- you can contact your county Human Services office- they can track where he works- even if he goes job to job-
He would be in contempt of court if he refuses to pay- so once you get a contempt order- he can go to jail.

(It's not REAL easy or fun or fast, but don't let him push you around.)

Good Luck
& keep pedaling!