K.M.
A.-
It is a very difficult situation. We went through the same thing in June. Our family dog of 2 years had bitten each of my children, and we had been working closely with our Vet on aggression issues with our dog. Then she bit my next door neighbors little girl. (She only ever bit in the house, when there was no adult in the room, she was terrific with our kids and the neighbor kids in the yard.)
I felt the same way you do. I struggled with the guilt of putting her down, but at the same time could not risk my children or someone else's children to be bitten. It is still hard when I think about her. My kids still talk about her sometimes. My kids are a 7 and almost 6 yrs old so they probably understand more than yours would being so young. I just sat down with mine and explained that she needed to be put to sleep, for the biting reason, and that she would go to heaven. That seemed to help them.
I hope this helps you.
K.