I am terribly worried about how my children will deal with our dog Eddie's death. I'm concerned with how they will cope with it. My eldest is 7 and my youngest is 4. They both saw our Eddie's body before we buried him, so they both got to say goodbye to him. Later I read them the story of Rainbow Bridge, and they talk about it quite a lot. I think it has helped them come to terms with losing him. In fact, in some ways they seem to be coping better than I am.
Believe it or not, in the scheme of things, this is actually a great experience for your children. The people who have not experienced death directly when they were younger can be quite disabled when it happens when they are older. It will not be long and you will see that you will all be better for having known and loved and "lost" Eddie! Eddie is giving your kids the tools they need to start building their ability to handle grief and loss in the future. It is an important tool to have in a world that brings loss the longer one lives.
I am happy to report that most children have plenty of diversions and are endowed with a great "imagination"(well, you think it's their imagination, the "fantasy world" they seem to live in, but it's just the memory they still retain of the world they knew before they came here). Your kids are still young and the fact that this situation has been incorporated into the fabric of their childhood will be a positive thing for them. You handled the situation with sensitivity and care. You have done everything right.
When human beings are born, they enter the world like us dogs do, We still have the memory of where we come from and where it's all leading (this life just teaches us and then takes us back to where we came from). Unfortunately, like us dogs, our babies cannot speak of it because they don't have language skills to do so (although many of them cry cry cry because the world they have come from is so much sweeter and softer and more comfortable than the one they have been born into! The terrible twos, by the way, are just the final letting go as they realize that they will be staying here on earth for awhile and That's That!).
Pets, as they grow, learn the rules from their master/owner/best friend. Children, as they grow, learn by copying the adults in their lives. Their parents and other family members and close friends are their role models. When your heart is pained because you see your young child crying, please keep this in mind. Often the underlying reason for the tears is that your child sees the adults crying and he is learning that this is the appropriate response to losing someone you love. It is more likely that he is copying or mimicking you than actually feeling the pain that causes tears. He is learning the ropes of living life from you. The only way he knows how to live is to copy how you live. Grieving aside, consider this in all that you do. The children are watching you all the time so that when they grow up to live their own lives they will know how to do it.
Children can be much more resilient than adults. As time passes, however, the babies turn into toddlers, turn into children, and ultimately become adults. As they develop they get caught up in the learning of How Things Are Done Here On Earth. This is why some of them have a very hard time in their teenage years. They still have a distant memory of the Way Things Are and yet the world around them drills into them, "No. That's not the way things work. You do it this way, not that way." They learn so much everywhere they turn -- at home--at school -- at work --- that they eventually incorporate the way they have been taught to live and they forget most of what they knew before they came here. This is why the concept of "death" is much harder to grasp when we are adults. We can't remember that Everything Is Okay, even death. The younger the child is, the more likely they are to know that their pet who has passed will be just fine. They still know that this life is just a dream. They haven’t forgotten this yet.
This planet earth is just a small part of the universal existence of life. When our pets leave, they are returned to Paradise, Heaven, the Rainbow, ether, other plane,.. It doesn't matter what you call it; it's all the same thing. The children know this. Do not worry so about them and take care of yourselves. Let the children teach you what you need to remember.
"And a little child shall lead them." Isaiah 11:6