I'll try to keep this as short as I can while being as helpful as possible. Firstly, pack theory is scientifically debunked. Your dog does not view anyone in the house as "dominant", nor as an "alpha". He knows you are humans and not dogs. If the dog listens better to your husband, it's either because your husband has spent more time working on positive training with him, or your husband has used strongly corrective training and the dog knows that disobeying means being punished.
Here are a few pieces of advice based on what you have described:
1. Your puppy most likely isn't aggressive. Sounds like he's a puppy and he plays rough. Aggressive characteristics are when a dog growls or bites at inappropriate or unpredictable times. So if he was calm and then you went to pet him and he lowered his head and growled, that's a sign of him being uncomfortable and fearful or aggressive. If you're near his food and he lowers his head and growls, that's resource guarding (which can turn into aggression). Biting and growling during play is NOT aggressive, unless he suddenly latches on to your arms, won't let go and draws blood.
2. It sounds to me like your method of training involves a lot of correction. Correcting a puppy without reinforcing a behavior you DO want is fairly useless. Yelling "no" constantly will get you ignored (as you are currently experiencing). When he goes to bite you or your children, grab a toy and redirect him to the toy. Praise him when he plays with the toy.
I got a great piece of advice once - "there are a thousand things you don't want your dog to do (nipping, eliminating in the house, chewing on furniture, dragging you on the leash, etc) and about 50 things you actually want your dog to do (walk well on a leash, play politely, not jump on you, etc). It's MUCH easier to train your dog to DO 50 things versus training him to NOT DO a thousand". So work on commands that directly contradict the behavior you want to eliminate. When a dog is sitting, he can't jump. So train a good solid "sit" and work on the dog sitting while it greets strangers to avoid jumping.
That being said, when your puppy is overstimulated and mouthing, sometimes no amount of commands or positive reinforced behaviors are going to get through. In this scenario, the best thing to do is to have a kiddie gate set up that you and your kids can step over to separate yourselves from the puppy, or to walk out of the room and shut the door until the puppy calms. When you say you bend down and pet him and he stops but then he starts again when you stand, it's because you have taught him that biting and growling gets him positive attention. He needs to learn that jumping and nipping means that all fun ends. Instead of yelling "no" at him, which is still giving him attention, ignore him and remove yourself from his reach.
3. 7 weeks is very young to bring home a puppy. I don't know any breeders I consider "reputable" who allow puppies to leave the litter sooner than 8 weeks. During their time with their litter, puppies learn the beginnings of bite inhibition by interacting with their litter mates. So it sounds like you have a difficult, overexcited puppy who was removed from his litter a little bit too early and hasn't been given any positive direction, only negative correction.
4. It sounds like a trainer could definitely be of use to you and your family. Please avoid trainers who use words like "dominant", "alpha", "pack leader", etc. Those trainers will teach you aversive methods that will repress your dog's negative behavior, but not eliminate it or teach him how to behave. Repressed dogs are dogs who develop unpredictable behaviors as they age. You need a trainer who will teach you how to work WITH your dog, to develop a healthy relationship with him that is based on positive training, not negative reinforcement.
He will grow out of some of these behaviors as he matures, but as with any dog, particularly giant breeds, it is very important to begin early and regular training so that you don't end up with a 120 lb adolescent dog who has no manners.
This is a fabulous article by Denise Fenzi, an amazing trainer, about puppies. It's a great read for anyone who has children and a puppy:
Its a Puppy, not a Problem! | denisefenzipetdogs
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