I just returned from Belize and spent a week in San Ignacio and can honestly say that I could have spent more time!
I stayed at the Aguada and Shala arranged wonderful trips including Tikal, Carocal, but you can do things on your own too. Just walking around San Ignacio you can go to Cahel Pech and Xunatunech on your own.
The caving at Barton's Creek is on the way to Xunatunech and both can easily be done in one day.
If you go to Carocal stop at Rio on Rocks on the way back since this is great swimming after climbing ruins.
Your kids will love the whole adventure and then wind down at AC before coming home.
Have fun!