Prince Andrew has been more or less persona non grata with the royals for several years,

[Ocelot II]

and his sleazy reputation and connection with Epstein is no secret in the UK. He no longer gets government funding, he can't use his rooms at Buckingham Palace, and he doesn't get government-paid security. His social media accounts were deleted, his page on the royal family's website was rewritten in the past tense, and his military affiliations and patronages were removed, and he also stopped using the style His Royal Highness. At this point there's not much of a reputation left to protect. So I don't think Andrew is much of a factor beyond the embarrassment that he already has been.

What's more likely to be going on is that Trump is being given the royal dog-and-pony show because the UK wants to stay in his good graces, and can use the royals' flattery to get it. They know Trump loves that shit, and it's probably all he needs from them to keep him happy. I'm just afraid he'll want even more gold bling than he's already tarted up the Oval Office with. Maybe he'll want the presidential limo adorned so it looks like Charles' royal coach. I'm sure he envies all the elaborate ceremony that surrounds the royals, but what he probably doesn't realize is that Charles has very little actual power. He, like the other European monarchs, is a figurehead, kind of a mascot. Sucking up to the King doesn't necessarily get him the love of Parliament, where the actual power lies. He probably also doesn't know that Charles' namesake and predecessor, Charles I, was executed by Parliament for treason.