How can I pay my half of the IRS tax debt and have my ex-wife pay for her half

Generally speaking, your divorce decree creates binding obligations between you and your former spouse.  It typically does not (and cannot) in any way limit a third-party creditor's rights against either you or your former spouse because the creditor was not a party to your divorce proceeding.When the parties have a joint debt obligation, including a tax debt, at the time of divorce, the court typically includes provisions as to how those debts are paid.  A typical provision begins with the language similar to the following:"IT IS ORDERED AND DECREED that Petitioner A.C. shall pay, as a part of the division of the estate of the parties, and shall indemnify and hold Respondent B.C. and his property harmless from any failure to discharge, these items:"This is typically followed by a laundry list of debts which may include 50% of any past tax debt of the parties incurred during their marriage.To enforce this provision against your ex-wife, you would first pay the IRS the entire tax debt, then sue your ex-wife for indemnity seeking a judgment against her for the 50% she was ordered to pay and to indemnify you from any failure to discharge.  You would then get a judgment against her, which likely will include interest and attorney fees, which you could then collect using any of the legal methods available for collection of an ordinary civil judgment subject to the usual property exemptions