This episode was very entertaining, but perhaps short on historical accuracy and maybe overly sympathetic to Margaret. Regarding historical accuracy, while its certainly true that Margaret and company traveled to the US and met with Johnson, its far less certain what, if any, effect her visit had on any change in US policy toward the UK, This episode portrays her visit as the singular reason President Johnson recanted his hostility toward the UK and approved the IMF loan sought by the UK. Also, Johnson is portrayed as a pliable buffoon susceptible to the charms of the British princess. Johnson was a master at manipulating others and it is hard to see him as being so easily and openly manipulated here by Margaret. He had many flaws, but he was not the fool portrayed here. Also, though Margaret was not without her charms, she just wasn't that smart. None of them are, and they are in general poorly educated. They may know what fork to use and which wine is best, but that's about it. While it is plausible that her visit may have played some minor role in Johnson softening his position on some UK-related matter, portraying her visit as the singular basis for the critical US policy change portrayed here is untenable and incredible. See Caro's Johnson books if you want a more fulsome explanation.
Regarding the presentation of Margaret here as overly sympathetic, as a counterbalance to this, I would suggest viewing:
This is a Tracey Ullman skit from many years ago that is just as entertaining today as it was back in the day. Whatever her reasons for being the way she was, Margaret was, by almost all accounts, insufferable, petty and obnoxious. Too little of that, however, came through in this episode.