Forget about what other daschunds you've known are like with children - every dog is an individual & needs to be monitored & treated as such.
Your son was an infant when you brought your dog home, & your dog was just a pup. This is actually the most likely reason you are having issues - dogs grow up & develop their personalities, and infants grow up to be annoying toddlers that intrude on a dogs personal space.
Your son may be as sweet as peaches, but if he is approaching the dog in a way that makes your dog feel "cornered" then there are going to be nips, as a warning for your son to back off.
I have worked with families who had dogs with behavior issues that they were able to overcome, by adjusting the reprimand to the dog. And another family had to surrender a dog back to me because there was no way to improve the situation in order to allow the dog to have a level of comfort in the home.
There are too many variables in your situation for anyone on this board to advise you on what to do. We can't see the layout of your home, the nuances of the interaction between your son & the dog, the effect that your current reprimand has on the dog.
At this point, you are faced with two options, with the understanding that it may lead to only one option, for the safety of your child & the well-being of the dog:
1. Hire a canine behavior therapist to come to your home & evaluate your situation, helping with training, boundaries and behaviors in this situation. This is not the same thing as going to obedience classes! They need to come into your home & see the situations as they naturally occur, in order to properly evaluate & advise.
2. Contact your breeder to return the dog & allow him to be placed in a home that will be more suitable. If you did not get your dog from a true breeder, you can contact Daschund rescue. Here are links for NC & Nat'l rescue. These organizations may also be able to provide you with resources for a behaviorist.
NC Rescue
http://www.almosthomerescue.org
Nat'l
http://www.drna.org
I agree with you 100% that bringing a dog into your home is a life-time committment. But just because you pick out one dog at one time, doesn't mean that it is the right dog for your family now. And as a breeder, I would much rather have a dog come back to me with an opportunity to be placed into a well-suited lifetime home, than have a family wait until it's too late, & bad things have happened, to the point where the dog has issues that make it difficult to find a good home, and have caused ongoing reaction issues in the dog.
Don't feel guilty if the right thing to do is to rehome the dog. He may be well suited for a family of older children, or a great companion to an older couple or single person.
If you have any questions, feel free to contact me privately.
T. (RR breeder 13 years)