I too am mixed regarding doing things with different hands - for finer movements (writing, holding a spoon) I prefer using the left hand, while for stronger movements (punching, throwing a ball) I prefer using the right hand. Not sure why though, I never underwent any "retraining".
I'm a leftie and that the same for me. I've think it's because the world is designed for righthanded people so we get retrained even if don't realize it.