Saga Blow up 2 Death Stars to Save the Day?

The Rebel Alliance has to blow up two Death Stars to end the rule of the Empire? Was it just because the Vader & Sidious were killed when the second Death Star blew up? If that is the case, then is Sidious was not destroyed with that second Death Star, Sidious would have created a third Death Star? But if they killed Sidious & not the first and second Death Star, then what would happen?

They blow up the first Death Star but then that does not end the rule of the Empire.

Then they blow up the second Death Star and that magically did the trick?

 

Yes

 

Killing the Emperor is what did the trick. Locking.