There is so much wrong here. Go with your gut. Your gut is telling you not to do this. So don't do this.
Trainers have to find the right method of training a behavior or eliminating a behavior that fits the dog AND the handler/owner. Your trainer seems to have little in her tool box, and does not recognize that she is not fitting you with what she is using. Especially since it seems to have no effect when you do it.
Frankly, if my trainer made my puppy cry, that would probably be it. Training should be fun, and keep a puppy engaged, and keep the puppy looking for more. There is just no place for puppies crying in training classes.
The whole idea of over-powering your dog to control it, is rarely necessary, kind of old school, typically counter-productive, and sometimes dangerous. I can't outrun my dogs, I can't out pull my dogs, and I can't out bite my dogs, but I can out think them. We have the human brain, and there are so many ways to teach our dogs what we want, that we really do not have to physically manhandle them.
Teach your dog the Gentle command. Use treats. Start with the treat in your open palm and tell the dog to take it but say, Gentle. Work with it. Use the word a LOT, and give it some time taking treats out of the open palm. A couple of days. Use the word GENTLE to remind the dog and GOOD GENTLE when he takes it nicely.
After he is really good at that make it more interesting. Put your thumb on it, and only let the dog take it if he is doing it gently. Continue to use the word to remind the dog before hand and to praise the dog afterwards with the word Gentle.
When that is good, progress to doing it with a closed fist. Good treat. If he licks the hand open and say, good gentle, dog gets the treat. If he tries to take it without being gentle, wait until he gives you gentle behavior, and then Good Gentle and give the treat.
When he is being gentle this way, move the treat to your finger and thumb. You are teaching the dog the term gentle. You are also teaching the dog to take something carefully or to inhibit the natural tendency to snatch it out of your hand and gobble it up. He gets it for being gentle, and when he can take it out of your exposed finger and thumb every time, gently, you are ready to use the term with other things. Gentle with my fingers. Gentle, whenever he starts to mouth. Good gentle when he pulls back and licks or uses his nose to get attention rather than his teeth. You can always remind him. Like when you get home, and he is excited, as you open the crate. Gentle with the old lady. Then he can be happy to see you, but he should remember to not put his mouth down on you.
I am sorry, but the idea of alpha-rolling a puppy for mouthing is freaking me out.
Bear Cub, Hepsi-Pepsi
Cujo2, Karma Chameleon
Ramona the Pest, Kojak -- who loves you baby?
Tiny Tinnie, Susie's Uzzi, Kaiah -- The Baby Monster.