Can you just call and make an appointment with the specific vet and say it’s to euthanize... don’t ask, just tell them.
We sortof ran into that at the emergency clinic when we brought Cartman in, who was obviously failing... she scooped him up and said she was going to go put him on oxygen... I said... no... that’s not why we’re here.
I don’t know how their hours work. But I’m going to call back and force the appointment and insist on talking to either the vet that saw her last or the surgeon.
I’m pretty sure this is the same woman who couldn’t diagnose our other cat. The one who had a convulsion, jumped out of my arms and was dead before he hit the floor.