I just wanted to say that I can feel a bit of what you are feeling. My H is in the AF and is actually in Korea for his year. We have 3 little boys and I'm here w/ them by myself.
Anyway, my sitch was my H dropped the bomb prior to his leaving. We were only "ok" for about a month before he left.
I honestly think the only thing you can do is be completely positive when you do talk to her at all. I also may suggest writing HER a letter telling her how much you love her (not begging), but get it all out there -- how you feel about her, that you want to work your M out, etc. Obviously, don't let it be a pleading letter, but just a letter so she knows where you stand on everything. I know it sucks you are kind of in limbo for the time being and can't even attempt to "work" on things or DB in person.
As for the A, what's going to happen is going to happen. Hopefully once you get home, things will change and, once you start DB'ing, she'll figure out the A was just b/c she was lonely or something along those lines (not that that excuses it). My H actually cheated on me numerous times while he was deployed.
Also, you have the relatives in your court and hopefully they will have some influence on her as well.
Me: 38 H: 35 S4, S5, S10 Bomb 01/07 Wanted D - nothing would change his mind Numerous A's prior to D bomb; EA prior/during D bomb Piecing 04/07 Deployed for a year 05/07 Still Piecing 2010 M 11 yrs 05/10