My wife and I sailed for a year with our 6 and 10 year old boys - plus our two big dogs! The entire trip, which began with an 8 month restoration project and ended with Hurricane Ivan, was unpredictable and unforgettable. Unlike you, based on your question about circumnavigation, we planned to sail for 2-3 years or until we decided to stop - no destination in mind. I agree with my friends on camaraderie, you don't need to set lofty goals, just get ready, have the whole family participate and set sail. When you're comfortable, go off shore. When you're more comfortable, cross oceans.
Have a great trip - you and your children will have memories to cherish forever based on all of the challenges you've overcame and the friends you've met. Be safe and live for the family and the adventure.