My thoughts are that it is rather difficult to give any sort of informed opinion, when we aren't informed. Has anyone ever trained the dog? Seriously, did ANY ONE, especially in your household, ever make any attempt to work with the dog and teach it how to belong and behave within your pack (family)?
If you did not, then I would go one of two ways:
a) If you are unwilling to do what should have been done long ago, and take the time to actually train the dog proper behavior, then rehome it with someone who will.
b) Get some books on dog behavior/training (several, not just one---there are many ideas about how to train/technique, but they all have gobs of information that will continually hit the high points of dog behavior and WHY they do the things they do, or DON'T do certain things when they don't, and how the "alpha" dog behaves and the "lower" members of the pack behave, and how they communicate position within the pack, etc etc etc... )
AFTER reading a few books, get some dog training. Take a class WITH your dog and practice practice practice.
I may be naive, but I'm just not understanding what the vet is going to say. Either you will take the time to train the dog or not. ONLY if you have diligently worked to train the dog and still have zero success, would your vet likely have anything "new" to bring to the discussion. Are you supposing that there is a medical reason the dog nips?
4 years is a long time to have a dog not trained (which essentially means, most likely, that he has been unintentionally trained that HE is in charge). It doesn't mean you can't train him now, though.
And while it may be your husband's dog, or he may be the one who wants the dog, he cannot do all the training/teaching of the dog himself. Everyone who interacts with it (adults at least, preferably teaching the kids some things too) needs to be on board with the training. Otherwise, you will be sending mixed signals without even knowing it.
ETA:
We have a herding dog (a German Shepherd). She still herds the kids, but she doesn't use her mouth/teeth. She is the gentlest thing I've ever seen when it comes to her mouth. You can take food or toys away from her with no issues whatsoever. She is delicate any time she uses her mouth. The only kids I don't trust her being around isn't b/c I don't trust HER, it's because I don't trust the KIDS to treat her respectfully and I am concerned they might hurt HER. I've seen many a child be too rough with a dog with no regard for the dog's feelings or even acknowledging that it is a live creature that can be hurt (sitting on them, pinching, pulling, swinging things that can hit them, etc)... Just because it might be a herding dog doesn't mean nipping would be an ongoing issue.