It's life changing and difficult. But try and do a day at a time as you have been doing. Pamper yourself when you have some time to yourself, good food, steady with cigarettes and alcohol. Resting and not going to bed too late is important.
Do some exercise too, keep yourself well. Talk to friends and family, invite someone over for an evening in. Plan small treats for the weekends with the DC, cinema, eating out, a picnic, visit a friend/family, put a film on at home and all snuggle under the duvet, bake some little cakes, make popcorn, visit a play park....
Cry if you feel like it, it's therapeutic and normal. Get support when feeling low and upset. Put a bad day behind you as no day is the same.
Try and look forward to future plans, a holiday, weekend away, spa day, a night out with a friend/s. It may be in the distance but it will happen.
You will be alright, you have 2 children who you can make your life for, your family, enjoy them, they are your best friends and you can all have good times in days/months to come. You will become a great team.
I've been there and know how awful it feels in the early days. It does change. Take an hour at a time sometimes. Come on here if you want support, to vent, get advice. You will heal. All the best.