It's not rough. The point isn't to bite the dog. It's to show the dog that you're boss and you COULD bite him if you chose to.
Generally, you won't get bit. A new dog WANTS to know his place in the heirarchy of the existing pack. You're telling him that after he works it out with everyone else, you're top dog.
Any new dog that bites you must be disciplined instantly, firmly, in a manner you're comfortable with. And your response should be tempered by the dog's history: if it's a new puppy that's testing you, you must respond firmly, unequivocably. If it's an older dog that's been abused, you might roll his lips over his teeth and let him bite himself and you, while you say "No' gently but firmly. As long as his bite hurts him more than you, and you don't hit him for it, he'll stop. When he does, if you reward him with kindness and a treat, he'll begin to learn his new home is different.

I am a big believer in using pack mentality and physical assertion when training a dog. I want to echo the fact that the individual dog's history really matters, as does the dog's size.

My brother got a puppy a year and a half ago (or so), she is a) the most dominant dog I have ever seen, she tries to dominate every dog she meets, and every person. And b) she is huge, a Rhodesian Ridgeback / Pitbull mix. In that case you have a big, strong dog, with a strong head. She doesn't notice a tap on the nose, she's too big, and filled with too much puppylike exuberance. She is a really sweet dog, but always looking for the opportunity to become alpha.

My brother has had a great deal of success showing her who's boss. But because of her size, that means sometimes pinning her down, not knocking over, just laying down on top of her and showing her that you could knock her over and pin her down. You then put your head near her neck or ear, and tell her no, firmly. You let her up when she relaxes (submits).

The level of success has amazed me. Again, since she's so big, and full of energy, she can be a handful just to play with (70+ pound strong puppy playing tug gets tiring), so it was imperative to teach her to calm down. If you tell her to be "gentle", she will stop. Walk up to you, and either present a belly to be rubbed, or give you a kiss.

Using this method of training does have things to be cautious of. You have to remember that you can actually hurt your dog if you get too rough, though dogs communicate through physical interaction so if you are willing to, gentle biting can say more that screaming at your dog ever could, biting can also be a positive form of interaction (dogs bond with each other by nipping the lips gently). Also, dogs are audible communicators as well, so the tone of your voice needs to be consistent for the action. I've found that the best tone for stopping a dog is to sound scandalized, like you are shocked that they could even do such a thing. If the dog thinks you're boss, they don't want you to be shocked by what they are doing; unless they are pulling a power play, in which case you move to firm "I'm alpha, you will listen" tones.

To close this long winded response; remember you are not trying to push the dog out of the dog. Some dogs will always have alpha ambitions, but if you like the dog and don't mind constantly asserting your dominance over the dog, you can have a great relationship with them. Once a dog finds its place in the pack, they are (in my experience) happy there, but dog pack hierarchies are always changing, so some dogs think its worth a try sometimes. Also from what I've read, the benevolent alpha gets challenged less, so love your dog while showing them who is boss.

I thought you said you were working with a trainer. What does s/he say about communicating who's leader? Does she think its OK for Prada to be boss?

Our trainer told us about the bite on the nose method also..when he was a real little puppy we had to do it, sometimes it took two of us to get him to submit on his side. When that happened we used the bite thing. Now we also do a similar thing with our hand..put a little squeeze on the muzzle...it is a sensative place, you need to be careful though, because the dog might become afraid. Shibas are strong and very wilful...but full of fun. We don't want to break his spirit.