I don’t think we ever find out what happens to Rapunzel’s original parents in the fairy tale. They just don’t come into the story once agreeing to give their baby to the witch. In that story, they were commoners, not royalty and instead of going on adventures the prince just secretly visits her in the tower until the witch figures him out, tricks him and he’s blinded. Eventually Rapunzel and the prince end up together so she still becomes a princess that way.
I’m certain we’ll still have the two worlds story structure. I don’t think that’ll ever go away for the duration of the series. The special effects limitations alone require that Storybrooke remains.