Oh Shanna I am so sorry!
I don't want to knock on the dr's practice but the whole situation is entirely WRONG.
We give a pre-injection which goes into the muscle, the shot does sting, but only for a second and most animals tolerate it well. We usually prep owners that their pet might cry so in some cases we take the patient with us in back, give them the injection, and then bring them right back to the room. The animal then falls asleep in their owners arms.
The sedation sucks on the one hand because it makes their vessels disappear but even if we have to try different veins your pet feels nothing, they are asleep - they have no idea what is going on. Things don't always go smoothly but at least your pet isn't in pain.
I read a forum post on craigslist one time that someone put their 18yr old kidney cat to sleep. The vet placed a catheter and then euthanized the cat. I know what 18yr old CRF veins are like and I think it's completely ridiculous to torture the pet trying to get a vein while they are awake.
I've seen a few euthanasia's without a pre-injection. Some dogs start vocalizing and it is really hard to watch. Euthanasia solution is a lethal dose of anesthetic, so she probably felt a quick rush and went to sleep - even if she was gasping and looking around she was probably really doped up and really didn't know what was going on so I hope you don't feel guilty that she was tortured or that she felt herself dying. Obviously none of us know because it wasn't happening to us but when I had heart surgery and they gave me my pre-stuff orally all I remember is taking the medication and going to sleep, however I didn't actually fall asleep and was talking with my parents and joking around but I have no recollection of that at all.
The whole situation sucks and I am truly sorry that you had to go through that. I would be absolutely mortified if I had to be in the room helping with something like that. I know at my clinic we try to make it go as smoothly and respectfully as possible.