You're depressed because you see more of yourself and your situation than you thought you might have in the letters from the people at the site. It's a shock to what you've built up as the reality and uniquenes of your situation. A crack in the door. And it makes you angry. Consider this.
If your husband is an alcoholic, get him help; if he refuses, then you need to consider what is best for you and your children (i.e. the environment they grow up in). Make him aware that he is choosing alcohol or he is choosing you and the family. Has he always been a big drinker, or is this something that has creeped in?
The great thing (?) about falling out of love, is that you can fall back in love and experience the rush all over again. Right now, you don't want anything to do with your husband because the OM is in the picture and is feeding you things that feel good after so long of not feeling good. This is completely natural and normal. You will not feel like doing anything with your husband while the OM is in the picture -- basic human nature. There is no reason for you to feel like doing otherwise when this great thing is going on. (But really, at some level, it's driving you crazy isn't it?)
The fact that your H is making any effort at all is a good sign. He likely does want to make things better, but he's in uncharted territory and isn't really a natural at figuring out your needs -- and he's carrying his own catalog of hurts and questions that he needs help dealing with.
Pick up "His Needs, Her Needs" by Willard E. Harley Jr. (
http://www.marriagebuilders.com/graphic/mbi6020_needs.html) and both of you can actually identify the specific things that one another need out of the relationship in terms of everyday actions. A blueprint if you will. The small things really do add up to a whole.
Will it seem contrived at first? Yes. Does it matter? No. Things are awkward in any *new* relationship at first. And in a way, this will be a brand new relationship with your H.
95% of what we all do is habit. It takes about 3 months to establish habits. Once they're there, it's automatic. The key is knowing what habits to establish to meet one another's needs.
Look, it may be late, but it's never *too* late until somebody is dead. Nobody should be miserable in their marriage. Unfortunately, unlike a new car, marriage doesn't come with a manual -- so people are very adept at screwing things up when things start to go south in a marriage. It doesn't have to be this way.
Obviously, you value the marriage on some level (even if it's just for the kids), so perhaps it's worth saving the marriage -- even though you don't feel like it right now. You *do* have the capacity to love him again -- if he *treats you the way you deserve to be treated* and *you do likewise*.
It's not black and white (as you've alluded to before), there is more than just "stay and be miserable" or "cheat and be semi-happy" -- there is also "divorce, move on", "fall back in love with my H and be happy again" and many other choices. If you set your mind to it, you can do it.
You've been married for awhile, right? A little more time in thinking things through won't kill you. Give yourself permission *not* to make any decisions right now. Think about things logistically and from all perspectives -- even the perspective of the benefits of getting back with your H (even though it seems unlikely). Evaluate for awhile. Try reading some self-help books, *go* to a good marriage counselor by yourself, *go* to couples marriage counseling (if nothing else, to ease the separation) -- these things will be good for you, and ultimately, for your little ones.