I am quite cross-dominant - in some areas more than others. For instance, I consider myself right-handed, I write right-handed, I'd kick a football with my right-foot, but I play snooker/pool left handed and I'm more dexterous (sinistrous?) at some things with my left-hand. (e.g., I can twirl a stick much better left handed than right handed, but if I need to do precise motor movements I'd use my right hand). For things like sweeping or digging, I'm equally comfortable with either hand.
When playing piano and trying to relax and play fluently, one of my most common errors is that my left hand starts to play right-hand parts, or vice versa. I'm sure there is an element of this for all piano players, what with trying to do two things somewhat independently at the same time, but do any other cross-dominant players suffer especially from this? And what do you do about it? (if anything other than practice, practice, practice!)