My housemate's eighteen month old identical twin grandsons appear to be developing with opposite handedness - one is using his left hand predominately the other, his right. It will be interesting to see how they get on when they start writing.
When I started playing I found I had to think about finger placement a lot for my fretting (left) hand. At a certain point that became unnecessary as my left fingers became quite nimble. I believe most people have the capacity to improve their weaker hand given the motivation. I find using PC keyboards helps a lot. It is a long time since I was a two finger typist. Over the years I have learned to use all fingers and both thumbs so my hands have to travel less over the keyboard.