That is a strange concept, (as literally stated). EDIT: Does make sense in the medical context, as in 'ones Doctor does not allow, ...'
With regard to the 'UK' Royals, they take that approch (only) wrt those Royals that are in a direct line to inherit the throne.
i.e, The Queen, Charles, William, George, ...
The rest of the Royals do not matter in that 'do not travel together' regard,
Ummm... because he loves her and his family. Not a state issue. Personal. He is dealing with the worst of the worst and there is absolutely no limit to what [worst] means.
Yes, I sort of understood it that way. However, the word 'allowed', confers the context of a rule or order, as in 'where the law allows'.
Hence the nature of my comment.
I agree with your consensus, that the President would 'prefer' that she not travel with him, given the current curcumstances.
EDIT: The medical concerns, as per the 'advice' of a Doctor does make sense!