Some of information that has come out makes it sound like this crossover will be three distinct but connected episodes, instead of one movie cut into four parts like Crisis on Earth X, so maybe the life swap is resolved in episode 1 and the next two episodes have some world hopping?
In the Arrowverse, Gotham City is essentially a failed city because the Batman has been missing for several years and thus crime has flourished.
“Our approach is: What does Gotham look like after the Batman has been gone for three years? So if you have the law and order, protector, and hope gone, what happens as a result?” says Caroline Dries, who consulted on the crossover and will executive produce the potential Batwoman series. “Some people are thriving in his absence because now they can start to do their own thing without the oversight. A lot of other people are suffering and they’re losing hope, and the city itself and infrastructure is falling apart. So it’s not a happy place. Our guys walk into a grimy, scary Gotham."
Outside of Gotham, there is a question of whether or not Batman is even real. In fact, Barry, Oliver, and Kara will argue about this in “Elseworlds.”
“Oliver is like, ‘He’s not real! They’ve made him up! It’s a hoax just to scare the citizens.’ Barry is flabbergasted by that and all he wants to do in Gotham is meet Batman. It’s a pretty funny scene,” says Gustin.