I am so sorry...that should never have happened.
I would get specifics from that office on how/why that happened...and then I would report the vet. I would not go back to that vet. I would definitely request to stay with your dog when you take her in on that final visit.
For what it's worth, I always hold my pets when they're being euthanized. I never thought that something like this would happen, I just think the pets are more comfortable knowing their human is near. Not judging...I know this is harder for some people than for others.
Again, I am so sorry.