Oh man- that is very heartbreaking. I get it- but I have experience from the other side too.
Our former vet (and my boss) found it very difficult to have the client in the room for the final shot- he took every death so hard. He would give a "sleepy shot" that put the animal into a very deep unconcious sleep, and the owner would hold their friend and say goodbye then- the holding and kisses would come while the animal was still aware. He preferred to give the final shot in the back, where I would find him on many occasions with a tear rolling down his cheek. If the owner wanted the body back, he would very carefully wrap the body in a clean towel, arrange it like it was sleeping, and carefully place it in a box (if the animal was small enough).
Most of the time, the final shot was very uneventful- the heart just stops, and the animal is in such a deep sleep that the shot is not felt. But I understood the way he preferred to euthanize- sometimes it is hard to find a vein, sometimes there is some disconcerting involuntary movement, most times the pets would eliminate, and the owner would completely lose it- not the way he wanted the owner to remember their pet. But sometimes it happens- the animal is unaware. There was another vet in the practice that was OK with the owner being present for the end, but I was present at a few that technically went fine, but the realities of death were completely shocking and angered the grief -stricken owners. It was those occasional not-so-pretty deaths that made me understand why it is perfectly acceptable and loving to say goodbye before the final shot.