If the milk tastes awful something in her mineral balance is not right - usually a drench with Copper should sort it. Staring coat is also sign of Zinc deficiency. To find that out would need however a blood test.
But if for example she had a heavy worm and possibly fluke burden as a youngster you will struggle to get her improved, as a lot of damage will have been done to liver and intestines. She just won't absorb much of her food, so whatever she is fed will go straight through...
However I would probably do the same as you and try to improve her condition....
I have a sheep that never grew beyond the size of a 3 months old lamb, is always skinny and skitty at the drop of a hat... and all because she had serious fluke infestation in that awful summer/autumn of 2012.... now I have a tiny sheep that's no use whatsoever... but she is still there