I love travelling, here are my thoughts
It would be easier for you to travel for only the 6 weeks of the school holidays, rather than a whole year, for the time off school. But prices are more expensive during school holidays.
How much are visas to USA/other countries ?
Cost of travel insurance for 3 ?
Cost of vaccinations for 3 ?
Your employer may offer a sabbatical, but they probably cannot guarantee that you will have a job to return to
There are Facebook groups for free home swaps Internationally. But this would stop you renting out your property for an income.
If you rent out your property, you will need to complete a self assessment tax return for the income generated to HMRC. You will need gas & electric safety certificates & landlord insurance. You will need money for repairs etc. What will you do with your possessions ? Who will manage the property while you are away ? If the property is empty for any time, you will still be liable for council tax & other bills. There is a responsibility, if you become a landlord.
The cheapest cost of travel would probably be via bus + accommodation or camper van in USA ?
It would probably be cheaper for you to go somewhere like Vietnam, Malaysia, India, Cambodia, Indonesia where you can get a room for less than £10 per night which includes breakfast for 3 people. Food & public transport can be bought cheaply too. Look on Agoda or Booking.com. You would need to check visa length. I have travelled to Asia a few times, but not longer than 6 weeks. You need to have your return flights booked at point of entry to the country.
You could look at teaching English in another country as a job for a longer duration idea
How much does it cost to live for a month now ?
How much would it cost to live in X,Y,Z country ?
Lots of planning & investigation to do
Most people do not do it, because it costs time & money. Plus you will be paying for 3 people
Goodluck