Can an employer deny health insurance coverage to an employee's children if through divorce the employee does not list them as dependents on his tax return?

Absolutely not! This is not legal. They are your children regardless of "who's turn it is" to claim them on taxes. I advise you explain this to HR and tell them that if not covered, you will have a lawyer contact them.

NOTE: As this is a "legal" question I suggest you contact the Insurance commissioner (or their title for your state) and have them provide you an answer for your situation, in your state.