V.W.
FWIW, if the court issues an Income Deduction Order for his employer to withhold the child support and send it in on his behalf, it is still valid even if he changes employment. So switching jobs shouldn't necessarily cause the support to stop---delay it periodically perhaps... but if the CSE workers are kept informed of his employment/employer then they can send the proper paperwork/documentation to his job to get the $ withheld without having to go back into court again.
They may well go back, for contempt, however... but they don't have to wait until then to send the proper notices to any new employer. They can also take his tax return. And file liens on any lottery winnings, etc.
I'm not sure why there should be that much carrying on about anything. Once support is ordered, that is pretty cut and dried. A court depository somewhere will have a printed out record of what he has and has not paid to date. (he's not paying directly to YOU is he?). The numbers don't lie. He either paid it all or he is behind.... you and your current husband are, quite frankly, irrelevant to the issue. Just ignore him. Do what you must, be polite to the court and let the CSE lawyer keep things on track (whether or not he paid). If you know of pertinent information (he has a side job or gets paid under the table, or won some sort of cash, etc), of course you'd want to share that with the attorney.