It is possible to develop ambidexterity later in life through more active use of your non-dominant hand. Most people practice by using the non-dominant hand to perform activities that require larger movements and then move on to small tasks using more control and precision. For some this is a lot of fun, while others may feel as though their actions are sloppy or in vain, but with time, patience and consistency the non-dominant hand can be used with ease or even equally as well as the dominant hand.
A part of the process of learning piano is bringing both hands to an equal level of playing. Many self-taught musicians come having learned to play only or mostly with their right hand. It is rarely a challenge to teach them how to play with the left hand, despite their perceived limitations. In fact misuse of the right hand muscles can require some un-learning and re-learning of proper right hand technique. So many times the hand that is perceived to be better may actually need a bit of correction or guidance, while the hand which was neglected has a clean fresh slate and progresses with ease. A good curriculum will teach piano students to play equally well with both hands no matter which hand is normally dominant.