What a sad situation. I can sympathise, having been in the position of having had to put down an otherwise healthy dog because her poor temperament made her a misery to herself and a danger to others.
I would though, first of all consider having a vet look at your dog. An older dog could be suffering some physical decline, such as arthritis, which is causing her discomfort or outright pain, and making her self-protective or irritable. I’ve read the Lyme in dogs can cause sudden onset aggression, as can some neurological disorders. If your dog has been an exemplary, if timid, citizen for eight years, there might well be a physical basis to her behavioural deterioration which can be ameliorated.
However, in the absence of a readily cured physical cause for her behaviour you really only have two courses of action; to make a major commitment to keeping her adequately confined away from other people, and supervised, constantly, for the rest of her life, or euthanasia.
It seems as if your wife is unwilling to make the commitment to constant supervision, so you have a sad choice to make.
If it’s any consolation, I think that dogs with this kind of innate fearfulness are rarely happy dogs. They live in such anxiety with such a constant awareness of inchoate threat, that even quite small changes in their environment are extremely stressful to them and can trigger aggression. You can’t reassure a dog who is afraid of everything.
Truly, your wife’s response seems really out of kilter. I can understand someone being highly stressed by the prospect of losing a beloved dog, but the corollary of that would surely be a determination to do what is necessary to protect others from the dog and thus a commitment to confinement and supervision for the sake of the dog and the humans…
My very uneducated guess would be that this is about more than the dog, no matter how stressful that situation is on its own. My probably presumptuous take on this, is that the my dog/your dog comment might indicate that this is about power in your relationship, with the dog symbolising something other than just her sad, hairy self, to your wife.
I wish you good luck in a very hard decision.