That is not how domiciles work. First, there is no such thing as a primary domicile, as that term implies that there can be such a thing as a secondary domicile (and potentially further domiciles). But that is not the case; you can have only one domicile at a time. You can have primary, secondary etc. residences, but “residence” is not synonymous with “domicile” (even though, for the vast majority of people probably, the two coincide).
Second, it is not true that you need to spend 17 out of 20 years in a place before that place becomes your domicile. You can always change your domicile to a new domicile of choice by taking it up with the intention of relinquisihing the old one. The 17-out-of-20-years rule applies only for tax purposes (https://www.legislation.gov.uk/ukpga/1984/51/section/267), not beyond that.
As for Harry and George, an interesting side effect of all this is that the Crown which George inherits also includes, among other things, the title “King of Canada”. If Harry’s domicile in Canada prevents him from carrying out the regency, I wonder if that has an effect also on the Canadian monarchy, leading effectively to a split between regency in Canada and in the other realms. I would think it wouldn’t, since (according to Wikipedia) Canadian law includes no provisions for regency during the minority of the monarch, so I suppose the duties of the monarch would just be carried out by whoever is regent under the British Regency Acts, also in right of Canada. In practice, it would not matter for acts under the Canadian constitution which are carried out by the Canadian governor-general as representative of the monarch, rather than the monarch personally; but I suppose it could become an issue for acts which the monarch must carry out personally, such as the appointment of a governor-general for Canada.
Yes, yes it is. There can be up to three domiciles under English law, the domicile of origin, the domicile of choice, and domicile of dependency. All three can exist simultaneously and often do. A person cannot hold more than one at a time, which is the primary domicile.
Second, it is not true that you need to spend 17 out of 20 years in a place before that place becomes your domicile. You can always change your domicile to a new domicile of choice by taking it up with the intention of relinquisihing the old one. The 17-out-of-20-years rule applies only for tax purposes (https://www.legislation.gov.uk/ukpga/1984/51/section/267), not beyond that.
Domicile law of England and Wales is complicated, but the tax rule while stricto senso only for tax purposes, has been used to determine for other cases.
Statute trumps everything. Until they enact a new statute. The law has been changed a number of times when the current law doesn’t produce the desired outcome.
Exactly. They did so during the minority of Elizabeth’s children, providing that in this particular circumstance, Philip and not the next on line, Margaret, would be regent.
Legally, yes. But although Harry might legally be the Regent, no one could force him to undertake his duties. I agree that in the case of a family crisis of the degree postulated in the OP, he would be very likely to agree to take up those duties. But should he choose to wash his hands of it and stay in the US, what could they do? Basically they would be stuck until they could pass a new law.
Which brings up the question, if you can abdicate as Monarch, can you also abdicate as Regent?
Actually, the most recent Regency Act says otherwise. The Regency Act of 1937 was amended by the Regency Act of 1953. This was back when Elizabeth was Queen and her children were the heirs to the throne but were minors (Charles was five). The amended law said that if Elizabeth died, Prince Philip would be the regent until Charles (or one of his siblings) reached the age of eighteen.
The law is now moot as all of their children are now adults (but it was never officially repealed). And it only specifically named Philip as a potential regent. But it did establish the principle that the regent can be somebody who is not in the line of succession.
You can’t effectively abdicate as monarch, except in the sense of “indicating a wish not to be monarch”. You remain monarch unless and until Parliament enacts legislation to remove you from the throne. Because this is legislation concerning the succession, it can only be enacted with the consent of the other 15 countries in which the British monarch also reigns, so it could take a while to organise.
I don;t think the Regency Act allows the Regent to “abdicate” so, again, legislation would be necessary. But if the Regent (though domiciled in the UK) were resident abroad, he or she could presumably exercise the power of the sovereign to appoint counsellors of state to act on his or her behalf.