Padme fakes her death, takes Luke to Tatooine with Ben to arrange things with Owen and Beru, goes with Bail to Alderaan to raise Leia, assumes new identity, dies of natural causes, (or an accident) while Leia is still a toddler. Problem solved.
That would take too much screen time after the climax. That would take a whole other movie. Also, why would she leave Luke with Owen and Beru if she was still alive. Why wouldn’t she want to raise both of her children herself?