I would not want a guy who chose me because of an ultimatum, knowing "she" is out there, knowing it was such a tough decision! Yikes, how degrading. IMO either relationship is bound to fail. Both women (and you too) deserve a partner for whom they are #1.
For what it's worth, I agree with the others who said don't commit to either woman. Commit to your children. Do whatever it takes to be there legally, financially, emotionally. There are many many parents who are not couples.
Best of luck to you, and thank you for your service to our country.