I met a travel RN who had 5 kids , he traveled with wife and kids for 5 years and loved it. They homeschooled and went site seeing. They took the housing. He spent 1 year at a assignment in Florida and said it was great.
If you go to warmer weather the kids won't be cooped up , they can spend alot of time out doors. You can make it work, like everything, you just balance things, sounds like you are ready to go.