I have the distinct feeling that this movie could have been produced in the US, which, let’s be fair, they would not really understand how a succession crisis would work in Canada (Also, we have another Trudeau in office, so it’s not entirely unrealistic for a son to take over). Or if it is a Canadian producer, they likely over-simplified the process by which a son could suddenly be elevated to the position of PM, which… yeah, a movie isn’t really gonna cover how difficult that would be.
As I understand it, because she is the Deputy PM, she wouldn’t be allowed to replace Trudeau unless she lost her position first, which would basically mean the Liberals would have to lose government this next election. Only afterwards could she possibly run for party leader afterwards.