I just wanted to offer my condolences and say sorry that you're having such a tough time I unfortunately don't have any great words of advice having never been through something similar myself, but I have faith that everything will work out for the best.
As for your kids, children are remarkably resilient, my younger sister was only 13 when my Mom died rather suddenly, and while it obviously devestated her, she has grown up quite well-adjusted and managed to deal with it just fine (she's 18 now).