While I would never advocate copious amounts, alcohol is toxic to dogs in the same sense that it is toxic to humans (and, being much smaller dogs can only tolerate small amouts). Many mainstream and "natural" calming products contain alcohol as one of their main ingredients,
including this one, which is sold by many vets (it is 13% alcohol).
I have worked with rescue groups (including currently having 1 foster and one dog that I kept after fostering her for several months) and in shelters, my grandfather bred pugs, my mother bred rotties, my sister shows and trains champion agility dogs (you can catch her on tv at the national championships next month--YAY Jenn!!). I only say this to point out that I have extensive experience with dogs. I am in no way advocating anyone allowing their dog to get "drunk" nor am I advocating regular dosing. Having said that, I stand by the fact that a mild dosing is a tried and true old-time remedy.
Having said all of that, when I have had doggy anxiety issues,
my doggy psychologist has always prescribed Xanax combined (in a few cases) with an antidepressant and/or behavior modification training.
Oh, and I would never give alcohol to a cat-- they metabolize it differently (as they do many things) and even very small doses can be deadly.