With Harry being a UK citizen, Meghan a US citizen and baby Archie both, there are a few complications taxwise for the couple. For example, as a US citizen, any income Meghan earns globally will be subject to US tax. However, if they stay in the UK for at least 6 months of the year she will be able to apply for foreign income exclusion hence avoiding double taxation. If Harry wants to earn money independently, he may have to limit his time in Canada or even give up his UK residency to avoid being double taxed.
Also affected are claiming for Archie as a dependent, reducing the chance of Meghan gaining UK citizenship, the setup of a charitable foundation, US exit tax if Meghan decides to give up her US citizenship and more. Let’s hope they have good tax advisors!