It was long before that. A few weeks after Elizabeth secured her title she got a law passed to make sure her younger sister could never take her place as queen. This royal family is not for sissies.
I couldn’t find a reference in support of your assertion, and if you have one, I’d enjoy learning more about Elizabeth preventing Margaret’s ascension to the throne.
The story linked below is very diplomatic, but it sounds like Margaret was raised to be a spoiled darling and her hell-raising was along the lines of how Andrew and Harry have lowered the tone for the whole family. The Townsend affair was going on during the period you mentioned; so maybe that was one of Elizabeth’s reasons for wanting to prevent a divorced man from becoming Prince Consort, in the event she predeceased Margaret.
However, Elizabeth already had two children when she was crowned, and Charles would have been King, with a Regent appointed for him until he would be old enough to reign.
https://www.biography.com/news/queen-elizabeth-ii-princess-margaret-differences