My deepest sympathies on this terrible experience. I'm sure the vet was upset too as I know the time I've seen it happen the vet was very upset. Euthanasia is not the part of their job the vets like much as they are all about keeping a pet alive and healthy.
What I've learned about this, when I went through it with one of my dogs, is that this can be a reaction to the body slowly taking the med in instead of speeding it to the heart and brain as expected.
Typically a little bit of medication is put in and the dog gets sleepy and becomes unconcious like it does with anesthesia. Then the rest of the med is pushed in and the dog's heart stops which ends its life. Because its already unconcious it doesn't know or feel that.
When the dog's circulation is not good, or they have a heart issue, then putting the med in may be uncomfortable as it builds up at the injection site, and the medication may not get to the dog's system at the speed it should to eliminate sensation.
The slowness of the med entering the blood streem can produce sensations that make the dog uncomfortable or that frighten the dog because they feel odd. It may not be pain just 'odd' and so scary.
The medication can also cause involuntary vocalization as a part of it taking hold slowly. The lungs are working but the vocal cord control may not so exhaling can cause vocalizing.
Now that I know this can be an issue, I usually discuss it with my vet and ask if the dog's circulation will support using a rear leg vein for the injection or not. If the carotid artery in the neck is used, rather than a rear leg vein, the med goes in really fast and the dog can be gone nearly instantly, which is a bit harder to bear, but easier than the med working too slowly.
I'm sorry you have lost other pets but I'm glad you know it doesn't have to be like this.
If you have not seen www.petloss.com and the rainbow bridge story it may bring you some comfort.
I hope this helps you!