I couldn't read your post and not answer. I'll try and keep it brief.
Firstly, I wanted to reassure you that children are remarkably, amazingly, incredibly resilient. When my ds1 was born his twin brother died and I was totally incapable of functioning for a good six months. Ds1 was changed, fed and generally looked after but not loved. I was so afraid he'd leave me too I couldn't allow myself to build up any bond with him.
Somehow, despite this and all the grief he's had to cope with in his short life so far, he's thrived. Your dcs have had to face something so very terrible at such a young age, but they WILL get through it and they WILL understand why you're reacting the way you are. That's not to say there isn't a long hard road ahead - if I said it would be easy you wouldn't believe me, quite rightly.
Secondly, you'll be surrounded by people telling you it gets easier with time. In my very honest opinion - and I can only speak of my only experience - it doesn't get easier, it just gets different. Life is never the same again. It took me four years before I could even say my son's name without crying - but somehow over time a good day will happen, then maybe another, and you realise you ARE learning to deal with the feelings. I'm sorry if that sounds harsh, but I so hated everyone telling me what a great healer time was.
I wish you all the best I really do for the road ahead - get through it any way you can, whether it's getting angry, or sad, or whatever - just get through it.