max we lived there for 10 years, moved back to the UK last summer. DCs were born there.
Everyone has a different experience there as very much depends on if you work, if you enjoy that kind of climate (can get too hot and humid in the summer), if you will have the the means to get off the island on a regular basis, how close you are to your family, if family and friends will visit ( be realistic, it is pricey and a long way), how often you will get back to the UK, if you dive or will have a boat etc, if you have a fixed term you will be living there, if you are prepared to educate your children there and pay for it, will you be happy renting or take the plunge and buy, will you qualify for Permanent residency should you wish to stay?
There are plenty uK expats with young families, the community centre on south sound would be one place to meet other parents I think the play day is a Monday, there are a number of soft play places and mum and me type groups, you constantly bump into the same people so you do get to know people. There are active clubs like the rugby, sailing and tennis to also meet other families and the way a lot of the housing is structured you tend to meet other families I.e, in the shared pool.
You are right you can't stick the DCs in the buggy and get out, you will need to drive. Camana bay is where everyone heads as mostly pedestrianised and has two fountains to splash in, bookshop, restaurants, soft play (starfish village which is also a pre school) cinema and a gelato shop.
Beach trips to seven mile will feature frequently as again you are correct there is not much else to do there. a day trip would be a drive or boat to rum point which is another beach so same stuff different location.
I will say that living costs are extremely high, you need to be aware of just how high when looking At the salary package being offered as whilst it is not subject to income tax you will absolutely pay tax whenever you buy something as consumption based or when you ship something in or even receive gift parcels - yes kids birthday presents subject to duty including the postage!
We prefer natural, organic food and while you can buy it there it is v expensive and not always as fresh as you would like. utilities are expensive too, you need to factor in health insurance as well and the costs of getting off the island even just to go to Miami
Remember there is no John Lewis, no M&S, no Amazon prime!
Sorry bit of an essay, hope that helps, feel free to ask any questions on here or PM me