No rule about switching sides of the batters box, other than the batter cant step across the plate when the pitcher and catcher are in position.
Work on throwing strikes and it won't be a problem.
I find the whole unwritten rule/bush league discussions irritating as you are always focusing on what the other team does or doesn't do.
Focus on what you need to do and the rest of the nonsense will not matter.
Do they need umpires permission?