Us British would say the first if the doctor has (in the past) insisted that you will (in the future) spend the night and the second if you (in the past) spent the night because the doctor insisted. Is that not the same in the US?
Interesting, I wasn't aware that there was a such distinction in British English between the two. Thanks for sharing.
I would use the second sentence for both cases. If I needed to distinguish them, I'd probably add something like "last week" or something to clarify things.
I doubt very many people in the US would give it enough thought to distinguish between those cases. It would be ambiguous, and if the speaker were needing to be more specific they would explicitly add context: "The doctor insisted that he spend the night tonight".