thanks for the additional information. IT is helpful. From your description it sounds like the adult dog is just trying to teach the puppy doggie etiquette. I'm not there, but it does sound like it might be the case. Dogs are very tolerant of young puppies and let them get away with behavior that would not be tolerated in an older puppy or dog.
As puppies start maturing, the older dogs start reprimanding them when they exhibit behavior not acceptable such as pushing past the alpha dog for attention, taking the alpha's toy or sleeping their favorite spot, rushing through the door first or jumping on the adult dog in an annoying manner. A dog's way of reprimanding a puppy is to first growl and if the pup ignores the growl, the adult will lunge and nip at the puppy. In most cases, the adult does not connect with the puppy though if the pup continues to ignore the reprimands, the adult might actually nip a pup to show they mean business. This is exactly what a mom will do with their pups and is not cruel.
So far it sounds like your adult may trust your husband and you to stop the pups behavior but not the older kids. We normally will tell owners to let the adult reprimand the pup as long as they are not drawing blood since that is how pups learn how to interact with other adult dogs. If you do not want to allow this, then you have to leash the pup and use the leash to reprimand the pup when it does things it should not do such as the things I mentioned above. give a short tug to get the pup's attention and a firm "NO" since most pups know the meaning of NO. If you make sure the older dog gets attention first and move the pup away until the older dog has gotten attention and always make sure the adult is taken care of first, the adult may not see the need to reprimand the pup because you are. The children may not be doing that and thus the adult feels she needs to.
Now if she is growling at the adult children, that is not acceptable behavior at all. You might keep a leash on her as well. When she exhibits this behavior give the same short tug and firm NO. Each time she doesn't exhibit the behavior when she would before, give her a tasty treat like a hot dog sliver Do not use regular treats as they do not provide enough incentive. It should be a high value treat like the hot dogs or liver slivers. In this case, I would want you to start back up her obedience training and have the adult kids do the majority of the training and let them know that the pup should not be allowed to "disrespect" the alpha by doing the things I mentioned. They should reprimand the puppy for these things.
The puppy should also be obedience trained as well. This is the best time to train the pup. The following site is helpful for teaching you how to train your dog. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would start making your dog work via the Nothing in life is free program (NILF). It is outlined below.
These techniques should help take care of the problem. Perhaps your husband will be a little more forgiving of the adult females growls once he realizes that it might be her way of teaching the pup if it is indeed directed at the pup and not the humans.
I hope this information is helpful to you and you are satisfied with my response. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have .