Good on going out with friends - you got a response. GAL works for you. Apologize for the communication problem and keep moving forward. If he's watching TV all weekend, invite him to do something fun with you. Movie? Bowling? Indoor go-carts? work out together?
Drinking... Does he buy the booze himself or is it just in the house? You could try not keeping any in the house so he has to get his butt off the couch to go get some!!!
Are you seeing a counselor? Does the military have a support group for spouses? He might have PTSD. Unfortunately with that or with depression, you cannot force someone to get help. They have to do that on their own. But if you see a counselor, it might help you get through supporting him during this time.
As for the OW... you need to determine what you are willing to put up with. What makes you wonder if they have started up again? Is he gone without explanation or not where he says he is? Have you found any texts or e-mails?
When you are happy as an individual, you are in a better position to determine whether a partner enhances your happy life or weighs it down.
