I don’t know New Jersey well enough (I grew up on Long Island but that was 100 years ago) but lifestyle - like anything, it’s a trade off. The working hours are likely to be intense - but perhaps you’re used to that already. You will probably have a bigger house, but nowhere in Jersey is cheap so you’ll pay for it. Unless you prioritise location, you’ll be driving yourselves and your kids everywhere - with a stay at home parent that’s less problematic than it would be for most. Schools for the younger ones will be fine (hopefully), but the teenager will have a rough time of it as I and others have mentioned.
My mom has a $50 co pay so every time she sees her doctor and gets a prescription, it’s $100. I would guess this wouldn’t be as problematic for you as for her (and her insurance isn’t great - the deductible is also high), but just to be aware that it’s not likely everything is totally covered and with 5 of you that will matter. Food standards are much lower so you might want to consider eating organic or at least antibiotic free. I am always surprised at the cost of our food when we are there, but eating out is cheaper usually.
Just for us, the lifestyle here in Scotland is infinitely better ‘but’ we’d both be working in either place and neither of us would have the kind of money you’d have to all the things above would be harder. (I was also personally connected to several shootings so the gun thing was a massive encouragement for us to leave, I just didn’t feel safe)
Plus sides? Bigger house, new culture and fun things to explore, NYC on your doorstep, the ability to see lots of new places on the weekends (check your holiday entitlement by the way, I know it’s better nowadays but it’s probably way less than you have now so maybe worth negotiating on that especially if you are planning to visit the Uk each year)… living in the states can be really easy and fun if you have the money to enjoy it.
(and super gross to note this but you’ll likely have an easier time if you aren’t POC. ICE is a crazy time right now and my friends and family in the states have seen a lot of craziness I’d never have foreseen)