Sorry about your loss
I am so sorry to hear about your loss. We lost our Max in March to cancer, he too was only seven. He had an undetected tumor and was bleeding out when we took him in. We had him in the week prior and they found fluid in his lungs and he was extremely anemic. We had to let him go that night and it was awful. We have a young Boston Terrier pup and she walked around crying for weeks. We were all such a mess. I have an 8 year old and 12 year old, we all fell apart, my husband was with him to the end. But time does heal and we quickly found a Boxer pup to add to our family. He has been the best medicine and keeps us busy and has brought laughter back into our home. We will always love and miss dear old Max, but life was not the same without a Boxer in our home.
Your kids are right about keeping busy, it helps. My kids avoided being home because it was easier. A great picture book that we all found very comforting was "Dog Heaven" by Cynthia Rylant. Try to get a copy, you may find comfort in it too! Hang in there!