I'm a pianist, not ambidextrous, and left-handed. It took many many years of practice to acquire the strength and agility that I had on my left side, e.g. shoulder, arm, wrist, fingers and acquiring it equally to my weaker right side. The initial weakness of my R.H. finger dexterity, in comparison to my L.H. finger dexterity, was the most difficult obstacle to overcome. Now, and only when I'm playing at the piano, do I feel ambidextrous with my playing apparatus, but away from the piano I still naturally do things that lefties do - I favor my left side just as right-handed people favor their right side.
Ron