Argh, weekends are tough, really bloody lonely. I remember that from before I came back home here. My email would be utterly dormant from Friday through to Monday, cos everyone was busy having a life, while i was just counting off another day of the expat sentence.
How old are your DC?
My dad left us when we were in our mid-teens, My mum always thought that we couldn't be a family of three, but you know what? we were a family, just a smaller one. I have a better relationship with my mum than I would have done if Dad had stayed. And tbh, dad is soo critical, perhaps it's as well he did leave, cos he can, and still does, say the most idiotic things. In time things will get better, this is the hardest bit.
I know that having to explain things to people must be excrutiating, but you wouldn't have done it, asked H to leave, if it weren't absolutely necessary. Hold on to that thought, and know that it will get better.
Try and pamper yourself on the weekends then, if they are the toughest times, do things for you, things that make you feel happier.
Keep busy for now, you will get through this, your DC will get over it, and when you are happier in yourself, they will see those benefits, you'll be a better and happier person in the long run.
If it helps to cry, go for it, sometimes there is nothing else like it!