Welcome to the forum and good luck with your move back to the UK
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I think the main hurdle you will need to negotiate is whether your wife can qualify for a spousal visa to move to the UK with you (I'm assuming your children are dual US/UK citizens, but your wife is a US citizen only?). There are accommodation and financial requirements you must meet in order for her to qualify for a visa.
The main ways to meet the financial requirement are:
a) you have been earning at least £18,600 in the UK for a minimum of 6 months
or
b) you have a guaranteed job offer in the UK, paying at least £18,600 per year and starting within 3 months of you moving back, AND you have earned at least £18,600 in the US for the last 6 months
or
c) between you, you have at least £62,500 in savings, which have been held in your account(s) in full for at least 6 months.
There are a couple of other ways to meet the financial requirement (i.e. £18,600 per year in non-employment income, pension income and self-employment income), but these are the most common ones.
See here for information on the spousal visa:
https://www.gov.uk/join-family-in-uk/overviewand the financial requirement:
https://www.gov.uk/government/publications/chapter-8-appendix-fm-family-members