Didn't realize this was an old post at first and was about to respond with advice.
Wonder if these people kept the puppy since they never posted again?
Just for educational reference for everyone that might read the thread though, what was described was pretty normal puppy behavior and I agreed with LavenderRott and others. Owners escalated the situation by taking stuff away with no reward for the items being taken and hassling the puppy around feeding time. The nipping during play was normal behavior. My hands had puncture wounds all over them when Walnut was a puppy, she was a ROUGH player and it took awhile to get through to her that she was hurting us. It's also normal behavior for a puppy to do that to test the owners and see if they can get away with it.
I really do hope the people kept the dog though and worked through the problems
Michalguy, I would be concerned about a trainer that uses the methods you described. Giving tons of treats for being relaxed and submissive is ok, but getting her to that point by restraining her under the arm until she does so can cause aggression issues in the future. I might ask how much experience this trainer has and where she learned her methods? What you describe is similar to an alpha roll, where you force the dog to physically submit, and that is often a bad idea. It's not even a necessary tactic to teach dogs to behave or show submissive behavior. The dog shouldn't respect people because they can physically overpower them. What happens when you try to do this with a very large breed like a mastiff? It may work while they're small as a puppy, but what about when they try to challenge you in their "teenager" stage when they're much bigger? Other methods need to be sought.
The dog needs to be taught respect by not being given any leeway when they misbehave or want their own way. You should stay calm in all situations (as you said, when you get stressed, she gets more stressed. Or more likely she sees you get frustrated and sees it as a good time to challenge you). If you start to get frustrated take a time out. Put the puppy away for awhile and go get your head together and calm down. Trying to train and solve behavior when you're frustrated or angry is going to make things worse.