No, your ex cannot stop paying child support if he doesn’t see the kids. Child support and child visitation are two completely separate issues. Your ex owes child support because he is the father of children and has an obligation to help support them. He does not get to stop paying child support just because he does not choose to see the kids.
Also, you cannot stop letting your ex see the kids if he chooses not to pay child support.
Again, child support and visitation are two separate issues. If he chooses not to pay, you need to file papers with the court for enforcement. If you choose to withhold visitation, that could be considered custodial interference, and that could negatively impact your custody rights in the future.
If your ex does stop paying child support in Florida, the Florida Department of Revenue can take steps to enforce the child support order. Some of the steps that can be taken is directing your ex’s employer to withhold child support from their paychecks and send it directly to the Department of Revenue, suspending your ex’s driver’s license, intercepting tax returns, deducting amounts from unemployment or worker’s compensation benefits, placing a lien on a motor vehicle owned by your ex, garnishing bank accounts of your ex, denying a renewal of your ex’s passport, and filing in court to enforce the order. These actions will often result in your ex finally paying.