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He never goes a day without thinking of her - without looking up into the night sky, occasionally talking to her. He becomes especially miserable during the full moon, while his sister becomes stronger and feels more at peace. Whenever he sees his brother-in-law on the night of full moons, he can't help but feel a twinge of jealousy that he is capable of spiritual contact – whilst he himself goes about with his shoulders slumped and his hopes low. Every full moon he envisions her face, the way her eyes sparkled with excitement, the way her snow white hair perfectly complimented her tan skin, and the way her laughter made him feel as though all was right in the world. He cannot help but agonizingly miss her. All he wanted was more time, all he had to do was protect her and watch over her as her father instructed. He misses her.
Even though his beautiful princess has passed – her spirit lives on as the moon. She watches over him and she protects him. She sees his life changing and transforming as time goes on. She watched him marry Suki on a winter night, and made sure her moonlight shone vividly for them. She watched the birth of his and Suki's firstborn – a girl – and her moonlight gleamed with delight that his daughter was named Yue. She watched and protected the premature birth of their second born – a son – who was named Kedar Tui. She made special care that she shined the brightest for those three major events in his life.
He found his life to become filled with joy, happiness, and light he never thought it would have after Yue was gone. Suki made sure she always gave him the space he wants every full moon – unless he chooses otherwise. Though she never tells her husband, she'll often talk to Yue. She tells her how that night of her sacrifice evoked Sokka to become a man who protects and sometimes irritably overprotective. She told Yue how during one adventure through the Serpent's Pass Sokka told her he was overly protective of her because he was to not be able to protect someone he deeply cared for – later learning about Yue and her sacrifice and how heartbroken Sokka became afterwards.
One night as Suki was talking to Yue about her sacrifice and about Sokka's overprotectiveness, Sokka was talking to the moon as well. He was holding his own little Yue as she was fast asleep in his arms, whispering to her about the stories and adventures he went on with her namesake during the time he had with her. He wanted he his daughter to understand that she must enjoy all the time she has on this earth and the time she spends with her loved ones – because it can all be taken away in one breath. With tears welling up in his eyes, he looks out of the bedroom window and sees the moon in perfect sight – and the tears start falling down his face. The wind and snow of the Southern Water Tribe gently hit little Yue's window and Sokka can almost hear a faint whisper against the window, "I am always with you."
Kedar is Arabian for strong (because he was born premature), and Tui is the moon spirit (whom Yue sacrificed her life). The part about Suki talking to Yue about overprotective Sokka is from Avatar: The Last Airbender S2E12 "The Serpent's Pass".