Balance is a difficult thing to teach someone.
On a severe side hill, downhill, uphill lie, almost everyone loses their balance. The critical thing to do is maintain your balance and spine angle as long as you can, most importantly on the back swing and in the impact area. If you lose your balance after impact, it will not affect your shot. Once the ball is gone, balance or anything else doesn't matter. A good example of this is Arnold Palmer's follow-through.