Just caught up with this story. Regardless of Andrew's history or reputation, his brother, the King, is being mean I think. Yes maybe logically Andrew should move to a smaller house, but he has this 75 year lease, from the Queen, it's his home - he apparently invested millions in it when he took it on (and won't get that refunded if he leaves) and I also read one reason he's determined to stay was he wanted to pass it on to his daughters. So in some respects he's just behaving like any Father who wants to leave his home to his daughters. But there's probably also sibling rivalry involved, with Andrew being a second son. And thinking he should have some status (regardless of his antics) as a second son of the Queen - and after all she let him have the lease. So his brother, now King, is being mean to him. After all the Queen made sure her sister Princess Margaret had a nice place to live at Kensington Palace (as a single woman).
So I think partly Prince Andrew is just being stubborn, partly, as a grown man, he has every right to decide if he wants to move or not when he has a lease. Charles is being an unfair landlord (and after that Channel 4 Dispatches programme recently, that should be no surprise) and is also his brother! And partly it's emotion - if it's your home, it's your home and he believed it was for his lifetime and beyond when he took out the lease.
Charles has now cut off the money that paid for Andrew's security - to try and force him out. And that is really mean! Of course he needs security. Charles has a habit of leaving people without security (I'm thinking of Diana here - I've always said she would never have died if she'd still had proper security and drivers etc).
But Andrew would probably be sensible to accept the offer and swallow his ego. Frogmore Cottage is a very nice place. But Andrew likes his lifestyle and doesn't want to change and is probably even more determined to keep it when he sees his elder brother with Buckingham blooming Palace and owning everything as King!
This is all hypothetical as personally I'd rather abolish the monarchy altogether and have no King and no Royal Family.
But I do think the Queen would not be happy with Charles for cutting off his brother's security. I suspect Andrew is not going to budge - his ex wife is currently touring to promote a new book - they're probably trying to raise some money to afford staying there.
If it was me - I would be furious if a sibling told me to move out of a house I had a 75 year lease on and tell them to get stuffed. On the other hand maybe Prince Andrew has to accept that - he has no income and can't afford to stay there. But he will feel entitled to support from his brother the King and feel Charles is being disloyal.
Wonder if "The Crown" will come back on TV with all this!