:) yeah see that kinda proves my above theory. kids will use whatever hand "feels right" to them, for the task the are doing.

you were taught at a young age "left hand wrong bad!" so it's only human that you would try and "fix" your niece. because as much as you may resent having been taught this, it stuck in your head.
and knowing you, you were also probably trying to protect her by teaching her yourself before the scary mean people made her feel bad and wrong. or at the very least i could see something to that effect also cycle through your head. :D