This is very common, especially if he's just holding. This is how he'd play with his littermates and mother, so he's just socializing with you. Puppies pay attention to your emotional state, and are motivated to please their caregivers (dog or human). If you let out a loud "ouch!" and clutch your hand to your chest like you've been seriously injured, the puppy will start to see his action as harmful. After demonstrating you've been hurt, offer an open (flat) hand to the puppy (palm just in front of his nose), and say some command for licking, like "kisses," in a very gentle voice. He will pick up on the cue, even before he's learned the command, and lick your palm. At that point, give really warm praise, verbal and physical (scratching the ears, whatever he seems to like a lot). Do this each time he mouths you. He'll learn very quickly what is expected.

Now, this doesn't address the fact that puppies do need to teethe. Just like little kids, puppies lose their teeth. While those teeth are loose, they are painful. If you can give the puppy something to teethe on, that would be really helpful. Try freezing cucumbers or carrots (same thing you'd give a teething baby). An antler or other super-hard chew toy won't give the puppy a good way to wiggle his teeth loose, and might be less satisfying. So cold items they can get the tip of a tooth stuck in are probably best. Rope toys are good, too, but some puppies will eat these, so it just depends on your pup's habits.

I've always "brushed" at least weekly. I had a very very old school vet, who was awesome, and he insisted this is incredibly important. He's not one for trends, so this isn't a fad or anything, it's truly important.

That said, my vet did not expect all dogs to allow physical brushing, so he recommended enzymatic toothpaste. The best product right now is Virbac C.E.T. Enzymatic Toothpaste. It is malt-flavored, and the dogs think it's a treat. The trick is to get a glob on your finger, gently pull your dog's cheek away from his teeth, and stick your finger into the far back, upper corner of his mouth, depositing the glob right on his gums. This far-back corner is also where the saliva glands are. If you get a nice glob deposited on each side's gland, then your dog's saliva will take care of depositing it along the gum line. The enzymes in the paste then dissolve the plaque along the gum line, accomplishing the same thing as a physical brushing might. I've never had a dog consider this experience as anything other than me being super awkward about giving him or her a treat.

As far as resolving the behavior through experience/training, all the other posters' comments are great.

In addition to behavioral training, it is important to know what to do if you are ever faced with a violent emergency that could turn into a life or death situation. All of the breeders/trainers I know insist the best and only way to disengage two fighting dogs is to yank their tails extremely hard. It is possible that you could slip the vertebrae, or cause other significant injury, in the tail, but nothing that is permanent or cannot be easily resolved at your vet's office. When compared to the alternative, which is that the dogs cause fatal harm to one another, the tail injury is definitely preferable.

I should stress that this is a recommendation for serious, emergency situations. I think it's important to share, not because I would ever want to see you have to use this, but because I've witnessed a couple really horrifying dog fights, during which I felt totally helpless. After the second fight, which resulted in an intervening pet parent's arm being torn all the way through to the bone from wrist to elbow, I consulted every trainer and breeder I knew so I'd be prepared to step in if I ever saw a situation like this again. The tail yank is the safest thing you can do for all involved. Even fight dogs (those abused to the point they are "trained" to fight) are likely to respond to this.

Absolute best thing for this is Grannick's Bitter Apple Spray. It's totally safe, works like a charm, and doesn't damage your furniture, shoes, clothes, etc. Basically, it's just a flavored spray that tastes awful, and the awful taste sticks in your dog's mouth for a while after they try to chomp on your stuff. I've fostered many puppies, and this has worked for every single one.

Alejandra's recommendation that you give them an alternative is also very true. Of all the dogs I've cared for who chew, there have only been two reasons: 1) they needed to release stress or relieve teething pain by chewing, 2) they wanted attention. For the former, the best things are antlers (these are healthier for the gut, full of calcium and last forever) and pig's hoofs (this smell horrible, and make your furniture or whatever they touch also smell, but that's what makes them way more appealing to the dogs than any of your stuff - unless you have a really ripe gym bag).

All of this stuff is on Amazon, and at PetSmart.

Just like Laura said, dogs are similar to people as far as triggers for car sickness. A lot of people feel better in the front seat than in the back. There are a number of safe and high-rated seatbelts for dogs, so as long as you disable the passenger-side airbag, it might be most safe and comfortable for your pup to sit up front with you.

Take a look at Dr. Foster & Smith (http://drfostersmith.com) first for seatbelts. I really trust their products. If nothing there works for you, check out PetSmart, and then Amazon. There are a lot of reviews on the Amazon products, so you can get a sense of ease of use, quality, etc.