The issue is not so much what you will do with the actual nanny (if you can even milk her), but what would happpen to the offspring, especially if you sold her female kid(s) (any males would be castrated easily and then have possible uses as meat and/or companion) on in good faith to someone as a pet but said person, then does a bit of breeding or goat gets handed on to breed somewhere else. etc etc... and also if you do have to give up your goats will the person taking them on be as responsible as you are?
So I am quite adamant that the only responsible decision would be not to breed from such a goat and actually have her put down/eat her. This is my personal opinion as a pedigree breeder (and seller), so you will have to make your own decision. I think it is really difficult because by the time you get the fault they have been very good at "tugging at your heart strings...".