Loki is in his cell as he watches the prisoners file past.
LOKI: Odin continues to bring me new friends. How thoughtful.
FRIGGA: The books I sent, do they not interest you?
LOKI: Is that how I am to while away eternity? Reading?
FRIGGA: I’ve done everything in my power to make you comfortable.
LOKI: Have you? Does Odin share your concern?
[Frigga says nothing]
LOKI: Does Thor? It must be so inconvenient, them asking after me day and night.
FRIGGA: You know full well that your actions brought you here.
LOKI: My actions? I was merely giving truth to the lie that I’ve been fed my entire life. That I was born to be a king.
FRIGGA: A king? A true king admits his faults. What of the lives you took on Earth?
LOKI: A mere handful compared to the number that Odin has taken himself.
FRIGGA: Your father –
LOKI [losing his temper]: He’s not my father!
FRIGGA: Then am I not your mother?
[Loki hesitates, realizing that to deny Odin as his father, he must also deny Frigga.]
LOKI: You’re not.
[Frigga forces a smile, but there are tears in her eyes. She steps closer to Loki.]
FRIGGA: Huh. Always so perceptive about everyone but yourself.
Loki regretted what he had just said to her, shaking his head he tries to hold her hand, but it comes right through hers. As he looks down he says to her -I wish you weren´t just an astral projection-
-I know love, I will tell you something you had not thought about – Frigga answered him – Your father and I chose to be your parents, not even Thor can make that claim. Odin could have left you to die onJotunheim, or he could have given you away, but he chose to keep you because he loved you.
-And then he thought me jotuns were monsters – Loki spitefully answered.
-We both made mistakes, all parents do even when they have their children´s best interest at heart. I would give my life if I could change it, I knew we should have told you the truth long ago, but we … I was selfish and a fool hoping you would never find out.-
-I wish I didn´t, I wish I could still be your child- Loki says as he looks at her, tears on his eyes –But I am not your child, I am the monster aesir parents tell their children about-
-Oh Loki! You are still my child, no matter how many mistakes you have made, I still hold hope in my heart, that someday you will forgive us and forgive yourself.-
-I cannot do that, I am the monster, remember? No matter how much I try I will never be like Thor or Odin. I will always be the jotun runt. You taught me to hate them, why shouldn´t I hate myself for being what I am? How can I expect any of you to feel something other than contempt?
I tried to prove myself to him, to you, to Thor, and all I ended up with was pain-
-It was not the way, you know it. Destroying Jotunheim was not the way to prove anything, it was just you trying to get even-
Just as she had ended her statement her chamber door opened, it was Thor he finally returned from his mission. She casted her hand over her own blue gem fading Loki´s projection.
-Mother, are you all right? You seem disturbed – Thor asked her as he embraced her.
-Do not worry son, we always end up fighting- Frigga answered him with a sad smile.
-How is he? -Thor asks her as she looks into his eyes
-Stubborn, but that isn´t new.-
-No it is not, has he told you anything about …-
-No- Frigga interrupts him –He refuses entirely to talk of the matter. But let us to forget about Loki for a moment. How are you? Have you finally brought peace to the Nine Realms?-
-Yes, I have- Thor answers with a big smile.

Notes

As Thor Dark World story unfolds I see no point on telling you all of the story, which you already know so I´ll just tell you the parts I´ve changed and you can assume the rest goes ahead as the story you already know.