I had to have a baby rat euthanized (she was born with megacolon and she had just stopped playing and eating). I actually prefered going to the vet with her. I think my other rats would have been stressed/confused by a vet coming to our home. And I didn't even want to be present for the actual euthanasia. The car trip home let me think and helped me feel better. And my other pets were waiting there for me to hug and cry on. That was the only time I had to have euthanasia. (I didn't feel the guilt or regret I've heard people often feel, but maybe it was because I knew the nature of the disease, and she gave me every sign that she could no longer live with any kind of quality...)

But I think it is highly a personal matter, and you should do what feels right for you. Only a vet should administer/handle the drugs. But the time, place, and whether you are present or not is up to you. If your vet won't do a housecall, just ask around.