If i were you i would try to go to couples counseling and try and work things out and see what happens from there if you love her the way you say and im sure she does as well talk to her in person and tell her how you feel what you told us and see ehat her response is and see if you can get counseling together and then if all else fails maybe it wasnt meant to be. But atleast you no you gave it your all and you tried.
Being apart form your spouse is extremely hard, in any situation, I know it's very easy to lose that connection and feel lonely and of course to need affection from the person you love. I was separated for 6 months from my husband(former army wife talking here lol) when he was overseas and it was extremely hard for both of us, so i understand how it is.
Have you guys tried couple's counseling? it will most likely help to patch your relationship if you have an unbiased person helping you out.(never tired it but have heard many many good things about it) Of course you AND your wife both have to be willing to work for the marriage. And I would definitely suggest not having any more one night stands if you are trying to get back together, don't want to mess things up more lol
Hope it all works out for you :)
Why not take that compatibility and re-establish a connection... but only as friends?
Because, trying to be more than friends doesn't seem to be working out.