Well, $4,150/mth might go something like this: you're going to have some income tax to pay, but not much on $50k with four dependants, so say $400, rent is going to start at around $1,000, but you won't get much for that so let's say $1,200 for rent. Then vehicles: you pick up a couple of 5-6 year old vehicles for $8k-$10k, and are paying $500/mth in loans, but insurance is pricy to start with, so that'll be at least $250/mth, then tax, inspection and registration another $25/mth (average), petrol is cheap, but you'll find you use a lot more, so a tank full per vehicle every two weeks would be $300/mth. Food: costs more, for five of you a minimum $150/wk, and probably more, so $750/mth. Utilities: tend to be more than in the UK, in coastal Virginia you're probably looking at heating for four months of the year at a minimum $150/mth, and AC for six months of the year at $150-$200/mth, so let's say an average of $150/mth year round. Health insurance is going to be under Obamacare by next year, and heavily subsidized for those on low income, but the insurance cost alone will probably still cost (and I'm guessing here) a minimum $300/mth for your family (which is pretty good going when non-subsidized insurance typically costs $300-$500/person/mth! ), but then there are fees of several different types every time you go to the doctor, so with three children that could easily be $100/mth, and quite possibly more.

If my mental arithmetic is correct we have got a total of $3,975/mth, leaving $175/mth for clothing, vehicle repairs, traveling home to the UK, pension savings, college savings, etc.

Honestly it looks like your monthly income will barely cover your ongoing monthly costs, with nothing left for anything else. For a family of five looking for a comfortable but not extravagant lifestyle I think your gross income would need to be around $100k, out of which you'll pay a lot more tax and for medical insurance, be able to afford new cars (so greatly reduce the chance of having pricey repairs), and have money for clothes, pension, college savings, and air tickets home, etc. ..