I was wondering when this was going to come up, Sir Mark Thatcher, a criminal conviction and the US visa system:

US authorities refused Sir Mark’s application for a visa because of the
criminal record he received when he pleaded guilty in South Africa to
funding a plot to overthrow the president of oil-rich Equatorial Guinea.

They simply don’t like to give visas to people with criminal convictions. Fair enough I guess, it is their country, and while he is married to an American, father of American children, he’s never applied for a green card or citizenship (he really really wouldn’t like the tax laws if he did) so has no right of residence. Not surprised by the story, was, rather, surprised by the glib assurances a few months ago that he would be joining the family in the US. Not right after a conviction I thought, not now you’re not.