M.C.
I would get the rainbow bridge book.
I think whether your son says goodbye at home or comes to the vet depends on his personality. As a child, we had to have our elderly dog put down. I have always been an extremely softhearted person, so my dad knew watching it happen would be too much for me. My brother though, was very worried about the entire thing so he went to the vet so he could see how peaceful and easy it was.
I would be honest in explaining the situation; not try to gloss over the death like many parents tend to. I imagine there are several books explaining the concept of death at an age-appropriate level. Make sure kiddo know that it is because she is in pain and not enjoying life any more, and she will be happier in kitty heaven.
Sorry about your Rigby. :( it's always hard.