It's going to be really difficult, I think. I used to know a German couple who had a house here that they usede every winter. They also set up and ran a seasonal business here. They were applying for the green card lottery because they had determined it was the only way they were going to get in. You don't even have that option, as citizens of the UK aren't eligible. And all this was back in 2002, before things got tough.
Even if you were able to get a visa, your wife and children would be prohibited from working. I don't know what happens if they reach adulthood before being eligible to apply for citizenship. I think they might have to leave the country.
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