When you make the will, etc. ask about an 'apostille', or check the US embassy web page for this. It's a legal instrument that makes a legal document document effective/recognizable in another country, so it makes a UK will recognizable in the US. Think of it as an international notorization. Also if you're doing a UK power of attorney (for yourUS executor and your uk accounts and maybe it would concern your children if they're here), you want to look into it from the UK side.
I don't remember all the details about the apolstille, but after getting a UK will drawn up (US executor, UK accounts) I remember going to the US embassy and paying about $35 for it.
Because your concern is your children, I would be very particular about these issues. If the children are physically in the UK there could be jurisdictional issues involved but the right kind of pre-planning could take care of them