@Navysubmariner
Let's take a step back.
The DOD won't send your retirement to your ex unless you give them a qualified domestic relations order (QDRO) that specifies how much and so on. I also believe the DOD won't honor a QDRO unless you were married at least 10 years. So you will need to check with them to see if your current divorce order meets their requirements, or if you need to get some other paperwork from the divorce court.
Now under the current situation, you receive the entire benefit and send it to her, and you get the 1099-R and pay the taxes. The taxes you pay include both the withholding and the extra you might owe, it's all taxes you pay, even though you never see some of it. You are entitled to claim a deduction for the alimony, and when you claim the deduction on your tax return, you report your ex's SSN, and the IRS uses that information to see whether or not she is reporting the income on her tax return.
Whether you get a benefit of the deduction depends on your overall income and other tax situations. Whether your ex is actually required to pay tax depends on the amount of the alimony and her other income, deductions and tax situations. But when you claim the alimony as a tax deduction, the IRS will get notified of that income to her.
If your question is "Will I pay less if the money and the 1099-R go directly to my ex?", the best answer is "Maybe". It depends on your overall income and other tax situations. Another way of putting it would be, "You won't pay more tax that way, and you might pay less, but someone would have to look at your financial situation in detail to figure it out for sure."
