The Duke and “Duchess of Sausages” are a clown show from start to finish.
If he’s making the US his primary residence, does he have to be a citizen? I mean will he be paying taxes?
If he works here, he has to pay taxes here on US-based income. However, if he also pays taxes to GB, then our tax treaty probably allows him to count the amount he pays there as paid to the USA. We have tax treaties with most countries.
Meghan is a US citizen IIRC and is taxed by the US on her worldwide income.