If he is too worried about the other dogs this may affect his cognitive functions and thus his ability to learn. If you bring to a pet store, this may not be the ideal place; too many stimuli and too close to the other dogs. The first group classes are very difficult at first but some dogs get a hang of it, but I really think he may do better in private classes for now and then once ready he can gradually move on the group.
You do not need to show you are dominant, all he needs is to understand which behaviors are appropriate and which are not. If he is biting your hands and leash, this can due to the fact he is stressed and is re-directing towards you his tension, or it could be he finds it rewarding to do so.
You need to find an alternate behavior to reward. Find a good trainer that is willing to to do private classes and give you one-on-one attention. Best wishes!