The left brain/right brain trope is a myth.
I've always wondered where this trope left people such as myself. I do some things with my left hand, some with my right. I write left-handed, but I can't do anything better than chicken scratch with my right. My wife and daughter can write with either hand equally well, and neatly. My son is strictly right-handed.
I use a fork or spoon with my left hand, and when cutting meat, switch the fork to my right hand to hold the meat still while cutting with my left. But I throw right-handed, and can't throw worth a darn for anything with my left hand. I mainly use tools such as a hammer or saw left-handed, but sometimes when my left arm gets tired I can switch without too much trouble.
I'm left-eye dominant, so I shoot left-handed. But I can easily switch sides and shoot right-handed if I close my left eye and force my right eye to be the temporary "dominant." When I'm pistol shooting I usually switch hands with each reload just for the practice, and my accuracy seems to be about the same either way.
I handle the ukulele like a right-handed person would, and can't hardly imagine trying to play it the other way. If I pick out a melody on a piano, I use my right hand. My left just won't work well enough to do that. Which is nice, because I can write the music with my left hand while playing with my right.
So I'm not ambidextrous...not really. Is there a word for it? I don't know.
Also for the record I hold my pipe in my left hand and carry it in the left side of my mouth. Right-handed pipe smoking just feels weird.