Hi Jill:
With 10 days at Walt Disney World, you will be able to comfortably visit all four theme Parks:
Magic Kingdom,
Epcot,
Hollywood Studios, and
Animal Kingdom. With so much time and your desire for a non-stressful trip with your two children, I would not attempt to park-hop, and I would keep your visit to just one Park per day. I would dedicate two days at Magic Kingdom and possibly two days at Epcot, depending on how your first day at Epcot goes. Even with so much time at Disney World, you won't be able to enjoy every single ride, attraction or event that Disney World has to offer, but you'll be able to see plenty to have a wonderful vacation. You'll also have left-over days to visit a
water park, stroll along the shops, restaurants and attractions at
Downtown Disney, spend a day or two just lounging at your Resort's pool and maybe even enjoy some
watersports.
Have a relaxing vacation.