If you managed to drink enough apple cider vinegar to provide sufficient malic acid to dissolve stones, I would think you would be sick from it. You are talking at least a quart a day which is a lot of vinegar.
Why don't you just swallow malic acid as a supplement? You can buy the malic acid tablets at the health food store. Also, have you done a parasite cleanse? If you have had zero results from 2 liver flushes, you may have a parasite load in addition to candida.