Her mother was too aloof and laid back while she was serious about school. Plus from the sound of things it seems like they didn't want her to know the seriousness of her mother's illness.
It seems to me that giving away the piano and her key chain is her trying to let go of the past, but I guess we'll have to wait 'til the next ep to find out.
I did not cry! If it lasted 5 more minutes I probably would. So yeah, this episode was just too beautiful. Wakana daisuki, oji-san to oba-san mo! Waa that was just Aww I guess we all know what song is gonna be in the final episode