I appreciate any insight on that. After being gone for nearly 2 years, my husband is feeling overwhelmed with how taxing this puppy/toddler relationship is. He's seriously second guessing our decision as this lil guy is NUTS.
I said I'd talk a bit about puppy and daughter experiences. I'm finally making time to do so.
Actually, I am remembering that our younger daughter was born when Oji was already about four years old.
Our older daughter was here for Oji's puppyhood.
She also was around our previous Dobe, but he was already an adult. That was a real tough situation because he had a problem that to the best of our ability to figure was simply a mental problem – a screw loose, if you will. He was a very good working Euro Dobermann, and I loved him. He was very trainable and a good guard dog. He would, however, unpredictably "attack" people. The quotes are there because he never actually bit when he did this; but if the person did not instinctively jerk back out of the way when he did his thing they would probably have been bitten. Dax did this to my wife on three separate occasions, and to guests in the house including the mother in law

Anyway, we don't have to dwell on that other than to say that we had to keep our precious little daughter away from him with extreme strictness. It was harrowing to consider that she might not instinctively jerk back and save herself. On one occasion, I had him in the same room as her, and he started to stiffen up and get that far away look in his eye so I immediately placed myself between them (I was standing right there and watching like a hawk) and whisked him out of the room.
With Oji, (another working-line European Dobe, but from a different breeder) that daughter was probably about 4 when we came home to us as an 11 week old pup. I can sum things up by simply saying I run a tight ship. I know dog training very well, and have always done all my training myself. I'm not trying to be a bragadoccio but that really is the foundation for the successful and safe household. I develop structure and respect in the pup from the start. I have found that my Dobes have looked to me as alpha and they literally look at me when daughters got near him as if to say "Is this okay?" "Am I doing anything wrong?"
We do not allow dogs on furniture, nor do we allow children to lay down on the floor with/near the dog. Humans always have a physically higher position that the dog. Petting and interaction is done when the dog is calm. We don't allow even a paw to be placed on a human leg or foot. No pawing. We have the child work with the dog on simple obedience. We have the child sometimes feed the dog, having him hold a sit-stay while the child gets the food, places it down on the floor, then goes directly to in front of the dog and releases him to go eat.
As for when Oji was a pup, and the daughter was around 4 years old: We just didn't allow hyper play or activity from either of them when they were together. I honestly don't remember everything. It just all comes naturally with the, well, tight ship I run. I know I may not be providing as much helpful specific information as you might've hoped.
Nipping?
Well, Dax's breeder advised something that I know you don't want: Just allow the nipping. Don't try to squash it. This was because the breeder very much wanted me to put working titles in bite sports on that Dobe. That is an accepted method. I don't think it apples to you though. Actually, I think we caved and went ahead and started to condemn the nipping/mouthiness with Dax. Wife getting nipped unchecked was just not sustainable.
With Oji, we condemned the nipping. You just establish a no command and enforce it. It is difficult! There will be nipping, and it seems like it will not end. Trust me, they outgrow it. Some might consider wrapping your hand around the pup's snout to deter/punish. Often, a spirited dog will just put their paws on your forearm and wrestle out of this.Some people suggest saying a dramatic "Ow!" I'm not so sure this is effective in working dogs like the Doberman. It might just excite them. You could try though. Some say deflect the behavior and redirect to a toy or suitable thing for them to mouth. Giving the dog the cold shoulder until they are not nipping anymore for a few minutes might be effective. No play or nice things come when the pup is being nippy.
I guess it's possible that your puppy is more hyper and problem child than my last two Dobes, but I kind of doubt it. You clearly are an intelligent, owner who is trying to do things right. That puts you way ahead of the average person. Things will get better.