Thanks for the additional information. That gives me a better idea of the situation. As you've noticed with your pup, some dogs don't respond very well to forceful or confrontational training techniques. Rolling a puppy onto his back can be very scary for the pup, and he may have thought you were attacking him so he tried to defend himself. In nature, the submissive dog voluntarily rolls onto their back to submit to a more dominant dog. Pretty much the only time a dog will forcefully roll another onto it's back is when he is seriously threatening the other dog.
You can use positive reinforcement to teach your dog most of what he needs to know to live peacefully with your family. Basic principles are to prevent or ignore unwanted behavior (as long as it's not dangerous), and reward the dog with praise, food, or treats for the behavior that you want. Since food is necessary for survival, it is one of the best motivators for dogs.
For example, in the situation where you are trying to keep him from going down stairs, instead of physically grabbing him, call him to you and give him a treat when he comes. You may need to start by teaching him to come to his name or the command "come" by giving him a small treat (1/4 inch or less) and praising him every time he comes after you call his name. With time, stop giving the treat every time, but always praise, and randomly give him a treat when he comes.
Back to the situation with the stairs..try to keep a close eye on him and call him to you even when he starts to head toward the stairs, before he starts to go down. You can also keep a short, light leash attached to his collar, and use that to guide him back up the stairs and back to you. In the beginning, use food or treats to encourage him to come to you instead of dragging him with the leash. Using the leash is less likely to trigger an aggressive response that physically grabbing him. If you can put a baby gate across the steps - that might also be an easy solution to the problem of him wanting to go down stairs when you don't want him to.
You can use this premise of positive reinforcement to teach just about anything. You just might need to get creative. Look at the situation and figure out what you want him to do instead of what he is doing. Then guide him to do what you want and reward him for that. Hope this helps give you a place to start.
Dog Veterinarian
4 years in general practice caring for dogs and cats