OK, so Harry has made it quitre clear that he doesn't want to live in England and wants no part of the family business.
It should also be borne in mind that Frogmore Cottage is part of the Crown Estate - not the Kings' personal property. Therefore it is not appropriate for it to be used by anyone who is - by their own decision - a private individual. Though the Duke of York is currently suspended from Royal business, he is still part of the organisation. The use of this relatively unknown and secluded residence as a 'sin bin' makes perfect sense. Windsor is more secure than the other Royal hiding place - Wood Farm on the Sandrigham estate, where Prince John lived until his untimely death in 1919. Andrews' proclivities and current unpopularity are such that he needs keeping an eye on, so Windsor is a better bet.
The King is in the process of an extensive reform of the monarchy and Royal Family which he had been urging on the late Queen for many years and which she had admantly refused to consider. He is not a young man and this will be his life's work. If he lives to see it done, he may well step aside and retire, passing the crown to William. His actions and intentions -including a slimmed-down and 'inclusive' Coronation - are already upsetting some people and I imagine he will upset a good many more before the end. He is definitely his fathers' son. So if he has to upset his whingeing, entitled brat of a second son, that's likely the least of his concerns!