Your dog will relax when you do some actual training. Work on obedience skills like heel, sit, down, come and a nice relaxed walk every morning. Even if he knows it all already, you do need to establish yourself as his leader. Don’t let him lead the way on the walk. Keep him beside or slightly behind. He will start to see you as leader of his pack shortly. With rawhide treats, start by asking him to fetch them to you. Offer a higher reward treat like the liver when he brings you the rawhide, and then let him have the rawhide when the game is over. He needs to relinquish to you so do this exercise with fun in your heart but be prepared to be firm too. When you feed him, ask him to sit and wait while you place the food on the floor. Don’t let him move to take it until released to do so. As far as handling by the vet goes, have strangers pet your dog’s body and face gently. Work up to placing fingers on and around his muzzle. If you give him a job to do at the same time, IE: sit and keep him thinking about the job (by reminding, “sit”, “sit”, “sit”) he has been given, he will relax. Reward with a treat every time he lets someone touch his face. Gently work your way up to looking at his teeth. Handle his body and feet while watching T.V. Keep your energy light hearted and positive. Unfortunately, vets get in a hurry and have an abrupt and business like energy that dogs don’t always understand. Help him learn to pull from your energy and look to you as his leader, protector, etc.
Teeth showing and fear are normal, but in a new dog pack it would not be tolerated. Indicate with a icky noise that you do not approve. When he is behaving properly indicate with a goofy happy noise. Big differences in tone will help him distinguish what his new pack expects of him. If he were in the wild, he would be making the adjustments to fit into a canine pack. Teach him your ropes.

Since the dog was a stray when he is eating he will be more aggressive because in the wild, dogs have to fight for their food and he may have seen you dad another dog trying to eat his food. With time and therapy he should get better with that. And as for the other events the dog may not like being picked up or have his mouth opened.

Dogs can show there teeth for many occasions, being hurt and them not wanting you to touch them, afraid, frighted, not use to humans, aggression towards objects such as food, treats or toys, ect. Just give him some time. He is unsure of some things, if you show him that he’s alright and that he doesn’t need to defend himself from everything he should start to come around. Try working on a little basic training so he gets to see that your not going to leave him like his last owner. Work on fun things like shaking or sit and reward him with really tasty small treats that he can quickly eat (which will help to avoid aggression to the food since it doesn’t last as long he will just eat it and have nothing there to guard). Just give him some time. If food aggression continues toward treats, just give him treats he can eat faster ( liver treats are a great training treat) and help him slowly come over his fears. Right now he just seems timid and seems to spook at things that are going on around him. Reward him when he is friendly and goes up friendly to people and just slowly work with him. You will have the most lovable dog, just give him some love and time.

It’s not normal behavior. In fact, the moment i bring in an animal, i make sure to feed them from my hand so that there is no question of food aggression. This animal could become more agressive as the time wears on. I always say it takes 4 to 5 weeks before you’ll ever see the true charicter of the animal.
Dogs never show their teeth to the alpha, period. They’d be kicked out of the pack for doing so. It could be this will get worse.
Sounds more to me that the dog showed his teeth in the car because of someone trying to help him. Trying to touch him when he was having some difficulty. Dogs do get overly protective when they aren’t feeling as up to par as they used too. But to show teeth is very disrespectful.
This is not something that will be easy to stop. Your father should not have walked away, he showed to the dog that teeth showing will get him the upper hand. Meaning, he’ll learn to use it more often. That you don’t mention he growled worries me even more. A non verbal threat is far more dangerous than a verbal one.
I’d say no more bones. I’d say start feeding him one or two pieces of food at a time and having the food be held in your hand. DON”T ask him to take the food from your hand. Get the amount of food you want to feed him in a bowl. Then pick up a handful of it at a time and hold it then drop two or three pieces at a time while he watches you, into his feeding bowl. He will be smelling your scent at all times and associating you wiht his food. You are sharing your food with him because you are alpha. Not because he is. You should also, always, make sure you eat before he does, your entire family. Dogs do not have to be fed at the same exact time every day and if he gets upset he isn’t being fed first, good. Let him KNOW that you don’t care, ignore the behavior and eat your food. Do this for several days, a month or two if you can stand it. When you don’t have time for it, get in and run your hands through the food extra well. Leave your scent on it all.
When you are done and the food thing is working out better, than you can try a bone again. You can get a larger bone and you can get your scent all over it. I know it sounds ooky but it’s important. Next, sit down on the floor and hold onto one part of the bone. Call your dog over and allow him to chew on the other side of the bone. The minute your dog acts like he wants to take it away, you pull the bone away and walk away with it. If he flashes his teeth, put the bone away. Safety is very important and i don’t want you to get hurt. If he does not try to fight you for hte bone, or jump on you for it.. it’s a good sign. After a minute, you can try again. And again, and again. Until he is happy he is getting any of your bone and nibbles it carefully so as not to offend you. Every bone, do this same thing. No bones of his own for at least 5 months.
After the first full week of food stuff, go and have him lay down beside you. Start touching him on his body. Play with his paws and nails. Play with his ears, play with his mouth. If he flashes teeth or acts like he’s going to nip you, stop. Dont’ pull back quickly. Say no in a very very low and short noise. Then slowly pull back your hand. Work very hard to not fear him. I dont’ want you bit, which is why i think you doing the food should happen for a month before you try this, but after a week or two you can give it the first try. Make sure you rub your feet on his bedding that he rests or sleeps on. Your bed, your stuff, your house. He just gets to be a follower within your pack. Your scent would therefore be on everything and nothing would be asbsolutely his.
Take him into the vet even when there isn’t an appointment. Get him used to the smells. Take in a treat he can eat from your hand and stroke him so and say in nice tones what a great place this is. This is a happy place that can help. When i have a dog that isn’t happy at the vet i start taking them evry day. I bring my own treats and i spend a minimum of 10 minutes in there each and every day. They get so used to the smell that it’s no longer a place to freak out on. They get so used to the treats and the extra petting they start to get excited to be there knowing their only treat for the day is coming. This is something that should be a good thing. To often people tense up and the dogs feel it and then they worry it’s a bad place. Or they had a bad experience. I practice lifting the dog up and placing them places. Like outside from the street to the curb. Often the vets is the only place they’ll be picked up at and that freaks them out if it happens only once in a blue moon. Or only when they are about to get a shot. So i do it often. Well, i have my husband do it mostly, but i actually do pick up my boxers as well. Not for a long period, but to quickly get them up onto a higher curb. Being picked up is no longer foreign or mean shot necessarily. I get them used to me playing around their mouth, and then i start opening it for brief moments. Then i look in there. I work them up into having their ears messed with, mouth’s, bottom and feet. By the time the vet comes they think it’s just another one of my things and are totally relaxed. You should really learn to get the dogs mouth open and get in there. Brushing their teeth monthly is very important to good dog hygeine. More often if you want the breath to smell good and their teeth to remain healthy.

You obviously understand a lot about dog behaviour! You are right about the adjustment part…He’s a senior, and he was adopted from the shelter…for the showing teeth part with the bone… dogs are very protective about their food. I was told once not to stroke or bother a dog when it’s eating…or it might think you want to steal his food and he was just doing that to warn your dad.