My vet came over when we let Mimi go at home. She was 15. Molly stayed downstairs with us since she and Mimi were the closest. We'd gotten them one month apart. Rocky and Maddy were upstairs because I'm pretty sure they would have been pestering my vet and wanting his attention - which I think would have annoyed Mimi. We didn't let the others see her after she was gone, and Molly never came over to look. She just stayed on her sofa and watched. They were all a bit off their food for a few days, but were otherwise OK.
Here in town we have a pet cremation service that will come to your home. They're wonderful folks who give the greyhounds a discount. I called them after I spoke to my vet and told them what time he was coming. The owner waited outside while we let her go and told us to tell him when we were ready. He brought a stretcher in the house with blankets on it and placed her on the stretcher and wrapped the blankets around and secured everything. I'm sure my neighbors were wondering what was going on if they happened to be looking. Kevin did help him carry the stretcher upstairs and put it in the car. It's wonderful how respectful they are of the body. A couple of days later they will personally deliver the cremains to you instead of you having to pick them up somewhere. I ordered Mimi a wooden box from them with her name engraved on it, and when it came in he brought it to me and transfered the cremains himself from the temporary box so I wouldn't have to do it.
I want to let the others go at home if it works out.