i think it would go like this:
Azula is in her cell, tied, bitter and full of hate, when she notices the door open. Slowly, Toph comes in with baby Lin in her arms.
Azula: what the hell do you want now!?
Toph: Shut up!
Azula notices the bundle in Toph's arms move and cry.
Azula: So you actually found a man to love you? Ha! i wonder who was the one doing the work.
Toph: no, i found a fallen princess
Azula fell silent and she noticed the tears on Toph's eyes.
Toph: Her name is Lin, your daughter!
Azula: That's impo-
Toph: what the hell do you think i said to myself when i found out!?
Lin starts crying harder, making Toph hold her tighter and shut her eyes
Toph: I want her to know her father...fire breath...but it's up to you
Azula, who never thought she would have a family of her own, looked at Lin and narrowed her eyes.
Azula: Do you think i would ever raise earth scum like you!?!
Toph leaves the room and never comes back, raising Lin on her own, with help from the gAang, and never telling anyone or Lin Azula was the father.