First off all, this song is most definitely connected to Young and Beautiful. If I recall correctly, Young and Beautiful was not wrote for Gatsby, another song was but they wanted Young and Beautiful instead, and I believe this was that song.
She loves imagery in her music, so the references to the hydrangeas and cars are likely to paint a picture for the listener. They are relics of an old time, much the same ways that "old money" represents an older generation. She talks about a love long lost, and her own identity which she can't get back - she'll never be "The Queen of New York City" in the same way that she was with the man a long time ago, she has moved on and evolved in a way that she can't reverse. I think she believes that the end of their love can't be reversed either, because even though she sings "if you call I'll run" and "if you change your mind I'll come", I always got the feeling in her tone that she knows its in vain because nothing will ever change, he will never come back, just like the glory days of "old money" are long gone.
Talking about her parents shows an example of a love that is strong and everlasting - the love she wants but will never get. That is why she feels alone, because she will never have what they do with each other with the man she is fixed on.
The repetition of the first verse as the final verse shows the cyclical nature of life and love. Kids grow up to be adults, much like Lana and her lover. Love grows, but it fades away with time. The kids don't realize how much their relationships will mean to them until they are older, like her. They are naive but in a beautiful, innocent, free kind of way. This is what she means by the "power of youth". This youthful ignorance is also something that, once lost, cannot be gotten back.