In most cases, the yeast infection is localized to the armpits, belly, etc. You need to bathe the dog´s entire body, then apply the vinegar, and then you can use the coconut oil as a more localized treatment. (If the hair loss/thickened skin is more generalized, it will need to be rubbed over the whole body.) One thing I always recommend with big dogs is that they are taken for a walk as soon as the treatment is applied. The coconut oil has a chance to sink in before they lick it off, and it is much less likely to rub off on your furniture. (Some of it does rub off, however.)
Not a perfect situation, I understand.