Sometimes its best to let your body get the rest and sleep that it needs peony and try not to feel guilty that you need to and that you arent doing things that you feel you ought to (difficult I know) at the moment I am sleeping over 12 hours a day and still not feeling as though I have had any sleep. Not getting any enjoyment from life is one of the horrible things depression does to you

I'm not surprised you have depression if you were in an abusive relationship, its a lot to cope with as well as a family and a demanding job, you know the real reason you had to leave your children, its best to ignore the girlfriend if you possibly can, firstly she only knows what she has been told by your ex husband and is probably going to be biased even if she was told the truth.
I know its difficult not to think of yourself of a failure after all thats happened to you but its the illness thats caused you to lose your job and your friends, rather than anything to do with your capabilities or your personality.
Its so very easy only to think inwards and get isolated when you are depressed, do you have any opportunities to go out (or do you feel you are able to) to find new people that you can eventually make friends with?