Unless money burns a hole in your pocket, I suspect that you won't feel any better or worse off than you do currently. You will just spend money on different things.
If you have a full expat package, you won't need to worry about healthcare, holiday entitlement - they tend to give you the best of both worlds. I know some people will tell you to be cautious about holiday entitlement, but someone on an expat package will not have just 2 weeks holiday. They will slot you in with your peers. It's the same with housing entitlement - you should get the kind of place that someone on your level has.
If your hubby doesn't work, he should make sure he makes voluntary NI contributions in the UK. Your company should pay yours as part of your package, but worth double checking.
The elephant in the room is your children - where they are educated and how they slot back into the UK. You mention school fees - is that so your children can go to international school? It's unusual for a company to pay school fees in the US as you would be living in a top school district.
As for living - you could easily replicate your Surrey Hills lifestyle. However, the US is very much a suburban nation, so if your really want to experience it, you would rent out a house in a swanky neighbourhood, with nice shopping nearby (it won't be walking, but neither is Surrey Hills). Your would join the pool club, and sign up your kids for all sorts of clubs. You can take all sorts of trips on the weekends - cities, beach, forests, mountains.
It's a nice and easy lifestyle when you can afford it, which you can.