If she isnt giving that much milk i would say its ok. Try not giving her as much food to make her make less milk. (pretty much what Farmer Kitty just said )
Use to but we have over 500 milk cows now so we pretty much had to switch to machine. We have a mixture of breeds but mostly Holestein (sorry about spelling if it was wrong)
Some people might not approve of this method but if the cow is really stubborn and you have tried everything else you can get a club and hit the cows lower leg on the opposite side that you are milking her so she lifts up that leg and she cannot kick you with the leg on the side you are milking...
Im not an expert with goats but i do milk cows and i really dont know what could be causing this.. I would have to see her in person. But I know that some cows are just born with one side of the udder bigger or works better than the other side. I actually have one cow that has only two tits on...