I think I feel similar but haven't had to go through what you've had to deal with. However, that sense of your life not being what you planned, it not being fair, that sense of injustice can just be overwhelming at times.
It's really hard dealing with your own grief while trying to support your children. Especially when they are less able to express how they feel and tend, therefore, to act out. I know how I feel and the impact that can have on my children when I am raging at the world. I do, at least, get some time 'off' from children and try to take time to grieve then. It makes for pretty miserable periods when I barely function but does allow me to wallow for a while.
The hardest thing to start with was my desire to disengage with life, which meant switching off completely and just hiding myself away. And away from the children too.
The children, in the end, started complaining. Which was really hard to hear given where I was but I have really tried to make myself more available. If nothing else, I try to give each child around 1/2 hour at bedtime for stories, cuddles etc. This has helped them, but it has also really helped me to re-engage with them. Also, the more engaged I am with them, the more I re-engage with life in general.
For me the sense of achieving things does make me feel a bit better. Even managing to get a wash on in the morning can change my perception of the day. I now try to look ahead a little bit and plan nice things for the children (and me, if I'm feeling particularly strong). Nothing big, more just like having a friend over for one of the children. It changes the dynamic a bit and I tend to clear up in case the parent wants to stay for a coffee - and if they don't I've still got a calm, tidy space!
This is all great, until I fall over, which is still a regular occurence. I try to keep to the bedtime thing (helped by a demanding DD 10!) which helps bring me back. It's not easy, I do try to take it a day at a time and at times I've had to take it an hour or even a minute at a time. But planning things does help, if only as it gives a sense of something to look forward to.
I took on a job (part-time) a month after we separated as we had no money coming in. On one level, that was way too early but it has also been enormously helpful. I have to put on a good face, I'm treated like a person in my own right (not wife or mother) and, if for no other reason, I have got to get up in the morning and go to work. It wouldn't suit everyone but it has been a really good discipline for me. It also means I have to be really organised the rest of the time which simply doesn't leave too much time to brood.
So I have learnt a lot about myself, some of which I already knew but had perhaps forgotten. I am resourceful, I am a (mostly) good-enough and loving parent, I am happier when I am achieving, I am strong and capable. I am a loving and caring person who needs to put myself higher up my priority list. I need structure to both my week and my day. I need to keep present and avoid activities that help me to dis-engage (telly being the worst). I eat when I am angry!
Only you know who you really are and what you need to do to re-discover the strong, determined, loving aspects of yourself. You are really hurting at the moment and that will not change for some time. As DD said to her counsellor who suggested she would get better 'No, I won't, it'll never change, but it will get easier and I will find a way to live with it.' Out of the mouths of babes.
Sorry for the long post!