Hi addledbrain.
Hope you're feeling better. Three months is no time, especially as you've had a new baby to cope with on top of everything. You sound as though you're doing really well not to have ground to a complete halt!
I separated from dp a year ago and still have down days but les and less. You will too.
These thoughts helped me; -
It sounds a cliche but just for now try to get through each day as best you can. try not to worry about the future. concentrate on yourself and leave dp to his own devices for now
Accept all offers of help - you must be tired and if you're tired you'll fell miserable. If it helps you cope go to bed with the kids and SLEEP. Try to keep one room in the house reasonably tidy so you don't feel overwhelmed by the chaos that two small children create,
Get out of the house once a day, even if it is just to the shops to buy milk.
Smile as much as you can when you think of it - sounds mad but it made me feel better somehow
Try to eat as well as you can and get some exercise each day, even if it is an exercise dvd or dancing around to music once the dcs are in bed
try to take pleasure in your time with friends and family and contact friends that you've lost touch with. consciously try to create a framework of support around you
Be kind to yourself - you are bound to feel miserable. Talk to yourself as if you were talking to a friend in the same position. If she told you she felt a complete failure you'd think she was wrong wouldn't you? You're not a failure
Tell yourself that you are a strong and lovable woman - you have not walked out on your dcs and you will be a source of strength and inspiration to them
Hope this helps a bit