So lets change the dog... Take the little nipper out of the situation and replace it with a doberman. To me, a dog is a dog, I don't care about the size of the mouth. Would you still use treats or retreat?
If a doberman were barking and nipping at my heels, I would do the same. Dog is already showing weak nerves and is unlikely to do much more than what it already is if you don't pressure them. Standing still and turning around to become less of an easy target would likely get the dog back to a respectable distance, and from there, you can again either wait for them to leave completely, or leave yourself (with the understanding that if you turn your back and walk off quickly, you will likely have a repeat of the prior behavior).
I have had a neighbor's roaming shepherd mix behave similarly, and he had actually bitten a few individuals on my block when they began to walk faster/run or kick at him. He never bothered with me because I didn't allow him to drive me, didn't run like prey, and didn't push him to the point that he would freak out in self defense. Animal control eventually picked him up and his owners never redeemed him because they had one of his puppies, I would imagine he was euthanized rather than placed due to his bite history and general sketchy behavior.
If I go to someone's house, it's not typically to police their dog's behavior. I have taken treats to peoples houses when I knew their dogs were reactive to people entering, with their permission. I enter, drop handful of treats, dog eats treats without barking or nipping, by the time that they're done, we (people) have settled and dog is good. Frequently those sort of dogs only react to people when they enter the house, and are fine once guests are settled and the excitement of their arrival is over. I don't particularly care whether someone else's dog "submits" to my presence or not, as long as it keeps its teeth off
me, whatever else it does is the owner's problem. My dogs wouldn't dream of nipping at a person's heels, and what other peoples' dogs do isn't something I concern myself with unless it becomes a problem for me.
Chas, If you can, I would work with your pup to condition her to allow restraint. Even if she's never the most tolerant of it, you can probably improve her tolerance somewhat. I'm actually working to condition one of my cats(!) to be more tolerant of restraint for blood draws, as she's on a low dose of steroids for allergies (she gets eosinophilic granulomas as well as general itchiness which makes her chew her hair off and puke it up everywhere :<) and should have bloodwork periodically. She is a nice enough cat, but turns into a bear when restrained to have something done. She is food motivated, and I'm giving treats as a reward for good behavior, and of course, release from the restraint is a big reward in and of itself. Initially, I was just calling her up onto the dresser and scratching around her neck, but now she's letting me stretch her out and tip her head up a fair bit without resisting (for jugular draw- the ideal but she says "no way!"), or I can put her on her side with minimal resistance until I stretch her leg out (less ideal blood draw site, but all we've been able to use thus far because she is a jerk). When she's at ease with the current level of restraint, I'll increase either duration or positioning criteria before letting her go and rewarding. One she has it down at home, I'll have to try it in the vet environment, then with other people involved, etc. It's been a drawn out process so far, but since she needs the blood drawn periodically, worth it to maybe make things easier for everyone in the long term. The training takes about 1 minute every evening as part of our usual routine, and I think now she kind of looks forward to her evening manhandling and treat
