See a lawyer on Monday.
See a tax lawyer and a divorce lawyer on Monday.
Two shots of Jack...
This is your problem. If he's taken up with another woman, and you're separated, you might as well make it a legal separation. Negotiate divorce terms and property settlements with your children's best interests in mind, and it should work out for the best.
The withholding doesn't matter very much, except that, if you're significantly underwithheld, you can owe interest at the end of the year. What matters is who is claimed as dependents on the return. You can't both claim your children as dependents, and he can't claim you if you're filing a separate return.
This seems like something you and your estranged husband could work out by agreement, if you don't wish to pursue a legal separation or divorce at this point.
If you are not even legally separated, the IRS looks upon it as you are still married, likely joint taxpayers. Best follow the advice of several Freepers here and get a good attorney, preferably a female with the personnna of a man eating shark.