Shining Inheritance comes to mind. The mother/daughter relationship between Chae Won and her mom is definitely interesting (if also dysfunctional).

Coffee Prince!  The juxtaposition between rich and poor isn't the main theme, but it is one of the many concepts that it covers.  Also, this is one of my all time most favorite dramas ever.  It was like crack for me, I watched it in a week I think.  

Goong (also known as Princess Hours) a poor girl enters the palace and has to adjust to life as a princess.  Also another one of my most favorite dramas. 

The Master's Sun.  Poor girl who can see ghosts latches onto a rich man who can make the visions of ghosts go away.
[quote]I'm interested in anything that shows a poor person striving for a better life.[/quote]
Queen of Ambition

[quote]mother & daughter relationships:[/quote]
for this one , i present you the best drama of all times :http://mydramalist.com/312-mother
The Best Lee Soon Shin
Birth Secret
Foolish Mom


[quote]father & daughter relationships:[/quote]
My Daughter Seoyoung
t's Okay, Daddy's Girl
Beautiful Rain
Two Fathers