N.,
First, I am sorry to hear you and your kids are going through this. It's never easy losing someone.
Just to share my experience...maybe somehow it can help...My Mom was diagnosed with an incurable, rare Cancer in 1999. After that it was a three year battle and struggle watching her slowly die. She was not herself at all when she passed away. I was 22. I was older and out on my own, but it was still like my heart was broken. I felt like a piece of me was gone forever. My 3 sisters (older), myself and my Dad were heart-broken, and deeply sad. It was the worst time in my life. I had a really hard time coping and it literally took me about a year to feel like I was living again.
I'm sure your kids are confused, hurt, feeling lost, and maybe even angry. They will need someone to talk to, separately would probably be best so each can share their feelings with an objective third party and not worry about what the other thinks. Do they have guidance counselors at school? Is there possibly a grief counseling service in the area for kids who've lost a parent? They may not want to talk at first, but it will help them cope and get by. Another suggestion is getting them a journal. They can write their feelings down on paper...just to have somewhere to get it out of their head and it may even help them heal. I journaled (still do occasionally) about the loss of my Mom, my memories of her, my feelings about losing her. I still look back and read my notes to remember that it does get better.
Lastly, just give it time. If they need to miss a few days of school to grieve, it could help. They may have a hard time concentrating in school for a while and may need encouragement from friends and family to get through it...as a way to take their mind off things.
Good luck. I really feel for you.