I can empathize with your situation. My H is also in the Military and they are a breed of their own! I read a book that really helped me, it is called Surviving an Affair, I believe the Author is Chalmers. I really learned a lot from this book.
My H has since answered all of my questions regarding his A. I will tell you that the push pull was because it was still going on. When it ended that push pull stopped. The I want to do things for you, but I still move some stuff out. My H did the exact same thing. Although he was gone for 5 months. That, I am leaving but not today is excruciating and I am sorry you are going through that. What I found is that when I truly DB'd and completely let go and was happy and content, he saw that. His A has its chance to bloom and what it did was withered. He found out the grass was not greener.
The problem I am having now is that I am not sure that I want this anymore and that scares me. I will tell you that I would be honest with your children and tell them the truth. Chances are they already now. My counselors said it was very important to tell my children the truth. As upsetting as it was they did find peace in knowing the real reason. I want them to grow up with honesty even if that means hearing things you don't want to know.
