Only a few years late Phatbeetle!
Not sure if the OP is here!
ArtsyChar, That does sound like a decent enough package and given the potential bigger economic and all the intrinsically linked aspects of the UK, Brexit, Jobs, immigration, Scotland wanting another independence vote, Northern Ireland wanting a referendum and Wales wanting one too, be glad you've got through with all the aspects of the package the employer is offering !
I used to work for 3 US IT/Consulting/Software Houses here in their respective London offices and met many, many staff who came over on transfers etc. Always a mixed bag, some absolutely loved it here for the short'ish period here, other's loved it for the longer term they were here, other's hated it within a few days/weeks, others hated it after a bit longer of a period. If I was pushed for a percentage, I'd say perhaps 60-70% of the ones here 'longer term' headed back 'relatively' quickly. I still know a few who've been here years!
I think nowadays, to get given a package like you have, you would need to be at very senior exec level and/or board level - which it seems you and your other/better half are. In the midlands, those benefits are going to be of more value given the lower costs of your household expenses. A similar family I met independently to my career contacts was in a rented house, sorry, mansion in the Wentworth Estate near Ascot, Surrey. Back in around 2007/8 ish, the rent for the property was around £20,000/month and they had all the schooling for the kids, cars, fuel, council taxes, food, bills and more all paid for! I think the salary paid didn't need to cover any of the mandatory outgoings !
There's some lovely places around Warwickshire and I think you'd have no problems really in finding an executive 5/6/7 bedroom property in a good/decent area. There's a lot of good info on this site for things to look out for and given a lot of your mandatory expenses will be covered, these will mainly be down to your family's personal lifestyle choices.
I'll also extrapolate a little more and say that the bank account they help with, will be a higher level or executive type account with specific benefits so do check those out etc.
Other than that, welcome to the UK!
KFDancer - look on the bright side, petrol is nice and cheap in the USA, you'll be able to get another M car
Cheers, DtM! West London & Slough UK!