as you all say, the amount of weight and terrain makes a big diff.
24 gear inches is really not bad, when I toured fully loaded, I changed my gearing so that I had about a 21 low low, and appreciated it many times, not a lot, but it was sure as heck nice to be able to go down 1 more equivelant lower than what I had before.

again, probably the 24 will be fine for not overly loaded , and yes, while 76 is not very high, it is again very doable as I agree with others who say they are usually in the 50-70 range.

My old touring bike has a 7 speed cassette, with a range of 21-about 103 gear inches, and that was fine for just about all terrain I encountered. Going to a 7 speed would give you a bit more range, and I suspect would not be expensive to do. (but dont really know the tech limitations ofyour bike)

as always, the easiest thing to do is to put a bunch of National Geographics in your bike bags and see how the sucker is on some hills near you. Im sure you will find that your setup is fine for light to moderate load, so have fun. An overnight trip will still be very exiting for kids.