So she lived in the village with her mother (who is the queen in the cartoon) who married the King?
So the long is her step father? This makes more sense. I've just seen the intro a few times and could never understand why it makes it sound like she just up and left for "her new family"!
The one hour special "Sofia the First: Once Upon a Princess" explains everything. It was the pilot for the show and the plot is basically the long version of the intro song.
I was really confused too until I watched it, then everything made sense.