Oh my goodness. I'm so sorry to hear this news.
Your boy will be devastated, but you will be too, I think?
I've lost a fair number of cats over the years, but only two were put down by the vet. (Cars and old age got the others.)
It's dreadfully sad, theres's no getting away from that. I don't think it's possible to soften the blow either, to be honest. It's about finding a way to be okay about the fact that we do it to them, rather than letting them die in their own way and time. That was the toughest part for me both times. Even though they're in pain, the time is right, it's kinder than letting them struggle on, and even though I support the right to euthanasia for humans, it's still a horrible thing to do.
Each time, I spent time with the cat and tried to talk it through with them/ with myself.
The vet stands as the person who takes responsibility for that choice, and they can be the person we give the blame/responsibility to. That can help a bit, and I suppose it's one of the many services vets do for us and our furry friends.
Each time I wanted to be with them at the vet. It felt wrong to make the choice and then not see it through. Cowardly, or not taking responsibility.
It's very gentle. Of course they know something's up, cos they're at the vet; and if they do pick up on our feelings, then they know something sad is happening. The vet gives an injection into the blood stream and quite soon they drift off and suddenly, from one moment to the next, the "person" of the cat is gone, and only the body remains. They're still warm and soft and furry, for a while anyway, but when you stroke them, it is different: the life is gone.
The vet will close their eyes and tuck the tail in neatly.
They do give you time to say goodbye, but they try not to drag it out and delay the inevitable.
As for bringing kitty home: I always did. My Ex chose not to, saying that the thought of him being buried in the garden would be too much of a reminder. Very pragmatically, the decision was made for the remains to be simply disposed of by the vet. I suppose he just went out with the waste. I didn't like that at all, but it wasn't "my" cat. A friend of mine brought her cat home and then buried him on Hampstead Heath. Despite warning her to bury him deep, she didn't dig deep enough and foxes dug him up that night, so she found his scattered remains the following day. A fox once dug down very deep - surprisingly deep - to get at a cat buried in our garden. We managed to chase him off before he got to the cat, and then raised a cairn over the grave. The people who bought the house later told me that they'd found the grave, and thrown the skull away. I was really very sad and cross about that. Unforgivable, I think.
Anyway the point is that if you want to bury her, you'll have to make sure the grave is deep and buried well. So perhaps cremation might be the better option if burial isn't possible.
Although I know of someone who buried her cat in a very large flower pot in her back yard.
How to square it with the lad….. I've left this til last because, honestly, I have no idea. Maybe a parent will come along and have something useful to say.