No offense, but maybe you and your kids just aren't cut out to be gold miners?
I did the Pan For Gold thing with family a few years ago at Knott's, and I still have the little vial with some decent amounts of gold in it. The 49'er running the location complimented me on my panning skills. I still keep the little vial on my bar, just in case I come across a cocktail recipe that calls for gold flakes.
But the thing I remember the most is the backache I was left with after hunched over panning for gold for 5 minutes. I ended up later at the nurses station for some aspirin, and she told me with a straight face that it's the leading cause of injuries at Knott's Berry Farm. Magical memories!