The Queen’s diplomacy to help get US support for the Falklands War is one of the more interesting parts of the video.
I tend to think the Brits overplay that.....ie the extent to which America was undecided as to whom to support.
Reagan was trying to play the part of an honest broker....to see if he could get the Argentines to back down without there having to be a war. After all, the Junta in Argentina at that time was anti communist. Losing a war over the Falklands was likely to topple them which the US did not want to see. So President Reagan held off on publicly taking sides while privately giving Britain all the military equipment and intelligence information they wanted.
For example, Britain did not have a Satellite over the region at the time. The US did. That was how HMS Conquerer found and sank the Belgrano. Once it was clear the Argentines were not going to back down and war was inevitable, Reagan came out strongly in favor of Britain.