Kevin,
All I can say, is you have my condolences in the loss of Belle.
You did the right thing by letting the kids spend whatever time they wanted to with her before burying her.
I know if Buddy (my shadow) ever leaves me, he'll be here on my property somewhere. I only lost one dog before, about 34 years ago, and she was buried out in the woods where she loved to roam.
I have had 2 cats that died due to Feline Leukemia. Both of them the vet took care of, at my request, because they were in pain.....terribly. But I never brought either one of them home. When I look back now, I would have done it differently. One of them was at my side constantly.....my gawd...how I miss him.
We now have a dog and 2 cats who are a big part of our family. It's just myself, my wife and these 3 around the house now. They all have their unique personalities, and we love them for that.
I have a spot all picked out, if and when that time comes, for any of the 3. And never again, will I EVER leave the vets office empty-handed.
Belle was very beautiful, she will be missed by you and your family very much.
Jerry