Don't give the IRS too much credit for catching simple things via edits in their system. Unfortunately, it's during an audit when some auditor sits down with several years worth of returns that things come to light.
Your tax guy should be asking simple questions as to who had the child more than half the year. At the end of the day, you have to substantiate your claim, and a parenting time tracker would be an excellent way to do that if you are ever questioned by the IRS.
In your case, I would be worried that your "tax preparer" does not seem to understand a basic premise of tax law that prevents two people from claiming HOH for the same child for the same year, and that IRS code takes priority over any court order that was not issued by United States Tax Court, or the Supreme Court of the United States.
Deciding to go forward with a divorce is kind of like joining a brotherhood. However, it is a brotherhood that you really don't want to join.