Belize with kids

No.

yes

Why?!?

Kids would probably like the Belize Zoo, Baboon Sanctuary, zip-lining and cave trips/tubing (I don't know if there is an age requirement on the latter two activities). Depending on your kids, they might like or be bored by museums and Mayan sites. If they snorkel, go to Ambergris Caye or Caye Caulker. If not into snorkelling, Placencia & Hopkins are good beach dstinations.

Of course, why not. All the places Mr.B mentioned are very nice, might enjoy the San Ignacio area as well.

Our kids would have loved Belize at those ages. We 1st visited when they were 17, 18, and 20 and we had 1 of our best trips ever. My photos with blog, travelogue, and review links on the main page of each collection are below in case you're interested - all my recommendations are embedded there.
Happy trails!
http://www.flickr.com/photos/staceyholeman/collections

you don't need to do anything. give the kids room to think for themselves

Also:
:: Don't move around too much (at least 3-4 nights/spot)
:: Try to avoid long car or bus trips
:: Consider having ac and/or water at each place (like a pool or swimmable beach or dock)

Laminated wildlife identification cards: http://rainforestpublications.com/belizeFieldGuides/index.html

A very cool checklist book for Belize for the young or young-at-heart (hard to find but maybe you'll get lucky): http://www.amazon.com/Play-Belize-Mesa-Somer/dp/0615198546/ref=sr_1_2?ie=UTF8&qid=1330549187&sr=8-2

Yes. I met lots of families while travelling there. I met one particular Dutch family in a few different spots. Their kids, 10 and 12 years, were having the time of their life.

I'd recommend zip lining, cave tubing, ATM cave. You could base yourself in Caye Caulker, San Ignacio and Placencia. I've no idea what your budget is but Ian Anderson lodge on the Hummingbird Highway could be another place to base yourself. Check out their website. They do lots of tours. Loads of families stay there (I was just there for the food).

Go for it, your kids will thank you.