I think I would rather have it done by a vet who had scheduled times for surgery that would not get pre-empted by emergencies.
I disagree with this. I wouldn't change vets because of a rescheduling of an elective procedure. I'd honestly feel like an equine patootie telling a vet clinic staff that I'm firing them because they rescheduled my dog's elective procedure because they thought saving the life of someone else's pet in an emergency was more important.
Most highly skilled, good vets take emergency cases for their clients, as they come in. Moreover, I want
my regular vet and the clinic staff to have the skills (and desire) to step into emergency mode if my own dog's life is on the line -- I've seen them do it, and they're totally different than when they're doing calm, routine appointments. It's a learned skill, honed under intense pressure when minutes count. It's very valuable when it's your
dog whose life is being saved. It also means your vet and their staff are under a lot of stress sometimes.
If a vet general practice vet doesn't take emergencies for their own clients during business hours, I would worry that it means they don't have the skills or staff to handle them. Good vets handle emergencies for clients as part of the long-term care relationship they establish. This makes practice unpredictable because you can't schedule emergencies. They happen in the early morning just as readily as in the afternoon.
Most clients really
appreciate having their regular vet in their corner when the unimaginable happens in life. In a small clinic, though, that means some routine elective procedures and appointments may have to be rescheduled because all their attention is focused on a dog in critical condition.
Instead of firing a vet over it, when you reschedule, I would tell the staff who calls to reschedule how much you appreciate them handling emergencies, and offer your best wishes that the other dog pulled through. Then have a conversation about your anxiety concerns.