Redoing insulation in the basement of the home I recently purchased

You put the vapor barrier on the inside of insulation to prevent cold air from getting near the vapor barrier. If warm, humid air is touching a cold surface, the water will condense out, just like you see on a glass of ice water on a hot, humid day. This condensation is a bad thing, since the presence of water over a long period of time will cause mold to grow. The moisture may reduce the effectiveness of your insulation. It may cause dry rot in your home. It may cause other problems, attracting bugs who like moist places.

How can you fix this? Turning the insulation to lie in the proper orientation is clearly the best solution.

I suppose one could put an additional layer of vapor barrier on the inside. That will stop the inside, moisture laden air from getting to that middle layer. The problem is, this will create a layer of insulation that does not breath. Any moisture in there will never escape, and you will have the same problems as I mentioned above. So this could potentially be a bad solution.

Better seems to add more insulation to the outside, with NO vapor barrier on it. That will prevent the cold air from getting near the vapor barrier. It may not be possible, or even terribly easy. But this is why you try to do things the right way the first time.

I'd use unfaced fiberglass, at least if each wall cavity has a place above the shower where the wall can breathe. Fiberglass is very permeable to air, which is why it only works well in still air.