C3PX,
technically in the moves when Luke and Leia were born, Padme was also a senator and no longer a Queen.
So I don't think she was called a princess because Padme used to be a Queen, rather because - as you said - according to the logic of Alderaan the daughter of a Senator was a princess. So the title was passed on to Leia by her adoptive parents, not by her real mother.
If Lucas had intended otherwise, this would create another plothole: why the hell isn't Luke a prince???
But since most of what Lucas came up with was really an afterthought (Luke and Leia - brother and sister; Vader as Luke's father, then as Leia's father too...) it's not much of a surprise that some things just don't make... sense.
About the "what makes you a queen" thing: what about the hair :p?
~~ Plagueis