I'm a left hander who can do most things with his right hand (and play right handed) but I have no problems with left and right.My dad has always had terrible problems with this - never forget the time we were in traffic, my mum asked which way, he said "left", we went left, got lost and during the ensuing row, he said "well you should have known I meant right when I said left"...
One difference between my father and I is that he was forced to do certain things right handed as a child - I wonder if that is the reason for his struggling.
Jon