I have only sent one from home. My first hound Future. Given the opportunity and circumstances, I would choose to do it that way every time. My vet (who has been my vet for 20 years) came out to the house on a rainy spring evening. Pooter was right in the room with us, Pearl watched from the next room. Both girls were just very quietly watching. It was as peaceful as it can get I suppose.
To answer the question, no the vet did not take my boy with him. We have a large property. All of our animals are buried here at home. My DH had already prepared the site beforehand. If I had my way, I would send each and every animal off this way.