Hi TC. Well, what an awful mess he has created and I'm sorry you got hurt in all of that.
He is obviously, now, not the man you thought him to be. Not only is he lying to you now, he is lying to this other woman so he can have a place to sleep. What kind of man does that?
Recovery is different for everyone, but basically he should be honest, with himself and others and be working on his issues, do you see any sign of that? Otherwise, if he is even sober now, he's just not drinking, recovery isn't entering in to it.
It takes a long time to recover, at least a year of help to get to any kind of sure footing (from all I have heard). Right now, getting any real, straight, answer out of him is probably pretty difficult.
I think you are right to file for separation. As for feeling "not good enough" please remember this has very little to do with you, if anything. This is his problem and his issue to fix, that doesn't reflect back on you.
I would recommend that you might want to read Codependent no more, by Melody Beattie, the most often recommended book here and really start to set some strong boundaries.
You may also want to visit our Friends and Family of alcoholics forum:
https://www.soberrecovery.com/forums...ly-alcoholics/