Can an ex-spouse use the threat of court action to force you to give them money above and over the current ordered child support amount?

Of course an ex-spouse can threaten court action to increase the amount they receive. People threaten each other every day to get something. Whether your ex-spouse is going to be successful in that action is a different matter.  If there is no basis for the action, they may be required to pay your attorney's fees.  If there is a basis, now may be the time to negotiate.  People are sometime reluctant to pay us $150 an hour to negotiate for them or to go to court, but over time, the cost may be a lot cheaper than the real cost if they try to do it on their own.