That should be a great cruise with a bunch of very interesting ports. In reality, it is two 12 night cruises back to back. Because of this you'll probably see a considerable change in passengers mid-way.
Don't worry about food as it will be good and you will have plenty of choices. There are shipboard activities for the children that should free up some time for you and yours.
I don't think that 'feeling herded' will be a problem unless you opt for a very popular excursion. Even then, the groups get broken down so they are mini-herds instead of big ones (LOL.) I have yet to feel like a member of a herd on any cruise or excursion.
I would spend a bunch of time on Google and learn more about the ports that you will be going to visit. Each one will have something of interest for both adults and children.
Enjoy your cruise.
Radiance of the Seas - Nov 2006
Legend of the Seas - Jun 2007
Costa Fortuna - Mar 2008
Legend of the Seas - Oct 2008
Celebrity Constellation - July 2009
MSC Orchestra - Jan 2009
Navigator of the Seas - March 2009
MSC Poesia - November 2009
Jewel of the Seas - June 2010