I believe you should let them use whatever hand they naturally desire.
 
I fit exactly your description. I'm left handed (writing with my left hand) but my strong arm is my right arm. I would through a ball, arm wrestle and do many other things with my right hand.
 
There is a common explanation to all this called Ambidextrous here is a link:  http://en.wikipedia.org/wiki/Ambidextrous
 
There are some sports that being left handed is a huge advantage, because most players are right handed (Tennis and basketball to name a couple) who knows you might be raising a future champ.
 
Best of luck.

Well, you can see which one they use better at sports. My daughter writes with her left hand and has more control and power in her pitches. She tries to use the right hand, but is not as good. So I tell her use the left. I would just observe for a couple of days and see.

This is something I've always wondered about myself.  My older son write left-handed, but throws right handed.  I am right handed, but have always kicked left-footed, and in karate, my left hip was dominant.  I do remember, as a child in the 50s, my mother "freaking out" when she saw me kicking with my left foot, and it wasn't a positive experience for me.
 
So I agree with member eliad.  Your kids know which arm/leg is best for which activity, and if it is or leads to ambidexterity, that might be all the better.  There are "switch hitters" in baseball who bat left-handed against right-handed pitchers and vice versa.  And there are some sports where ambidexterity is a necessary attribute - handball for example.
 
It would be interesting to hear from an expert on the cognitive and neurological mechanisms and implications of cross-handedness.