First, my condolences on your loss. In addition to worrying about your children, please make sure you get the support you need through grieving as well.
We have been through a lot of this lately at our house, unfortunately. We have a seven-year-old daughter, and in the last two years, we have lost two of her grandparents and three pets (of all of these, only one pet did not have a good long, life behind it, since he died of cancer). We also struggled with announcing and explaining death, especially since the concept is hard to grasp for a child of six or seven. We had tried to prepare her for these eventual outcomes, trying to set expectations, since the grands were close to 90 years old and ailing, and one dog was 16 and the cat was 20! Especially when one of them would struggle or get sick, we would lay some groundwork.
Nonetheless, it is always a shock, even when you know someone is elderly and/or sick with a disease. We felt honesty was the best policy. Life will have bad cycles, and there is no way to completely protect our children. The main thing we can do is try to handle this honestly and openly ourselves, so that we can help her deal with it, too. We have made sure that we discuss this, cry if we must, and provide times where it seems appropriate to reminisce about someone. We have had candlelight prayers at dinner for someone who has passed to make an additional ritual. Talking with others helps. I think one of the biggest thing for our daughter was to find that other kids her age were also experiencing the same thing. Sometimes they think they are the only ones. We also tried to emphasize that most of the time, people and pets die after living a good, long life. That also seems to help us somewhat. But we did not sugarcoat the fact that one pet got cancer and died.
One thing we did not do at her age was have her attend any funerals. Particularly since one grandparent had requested an old-fashioned open casket funeral, we thought it might be frightening for her. But she has been interested in visiting the pets' graves, and when we all feel ready, we will visit the last grandparents' grave as well. Since your children are older, you may want to give them the choice of attending or not. Funerals never really helped me grieve, but they are very healing for some people.
We have not gone to grief counseling or support groups, but that would be another option. There are usually groups in a local area, and there is even information on-line. I don't have the websites any more, but you can Google and possibly find something that would help your family situation. Hospice groups have materials that are a help. We find our church to be a great source of support as well. The last death was hardest, as she was close to the grandmother she lost. My mother is now under strict orders to watch her health!:)
Our best wishes to you as you work through this trying time. Healing will happen, but it will take a while. Just expect to have your ups and downs if you haven't been through this before. The one thing I have learned is that every loss is different, and the grief accordingly changes somewhat as well.