The problem with your mother's version, Boxtops, is that BOTH words, thither and yon, suggest towards THAT place, whereas we obviously need one to mean towards THIS place...ie hither.
I wasn't criticising your mum, ma'am, only pointing out that her saying didn't quite work. I didn't know that you realised that, of course. My own mother was the same, repeating half-heard phrases that were basically nonsense.