I have found the best way to dry off GG's is to divide their pens, and have kid still close to mum, but not able to suckle.
Having had to start milking my GG when she was on her second kid - it was a struggle, and even now I am the only person allowed to touch her udder, she goes mental (and I mean mental) on the milking stand if anyone else is trying to milk her out. Depending on how old your girl is and how much more breeding you want to do with her, I would probably follow the vet's advice and try to dry her off, but don't get yourself all worked up if it doesn't work. If she is really freaking out at the kid not being there, just leave her and try to find more/different food for her. Branches are the best, willow, some ash (not to much), hazel, rosebay willowherb once it is growing properly, birch etc etc. Nettles, cut and dried for a day or two are really good, fresh dandelions (flowers and leaves), dock leaves, sticky willy, thistles as well, all fed fresh also good.
To be honest if she has never been used to a wide range of feeds you will struggle to introduce new stuff to her now. A general vitamin/trace element drench should also help her (and she can't refuse that as easily as powdered ones!)
Johnes disease (pronounced Joonees, rather than John's) is also possible, your vet should know how to test for it and if it is likely.