The mane should lay on the right side, unless you ride western, then it's "supposed" to lay on the left. To me, unless you're showing rated shows, then who gives a hoot.
My guy has a little bunch that always goes to the wrong side and I kept his mane braided for 2 weeks last fall, but it didn't help. I always worry too about a braid getting ripped off. I might try those Mane Sox, like little tail bags for mane braids, because I'm going to try doing braids again.