Background Pony #FE37
Something just occurred to me: Why hasn’t Sunset gone back? Even if she wants to stay in the human world, she could reconcile with Celestia first.
Background Pony #B950
@Background Pony #E7F7
 
Everyone else is greeting twilight in the first EqG movie. Celestia is worried about Sunset Shimmer.
 
Also her cutie mark is well a Sun, Which means the Sun is FUNDAMENTAL to the essence of her being a representation of who she is and can be.
CronoM

@Background Pony #E7F7  
The way Celestia looked at Luna’s picture when she felt like she failed Sunset, it definitely makes the idea that at least their relationship was at its core, mother and daughter. Also, the way they used the words ‘getting past this’ in the comic when they fought did not sound like master and apprentice. It sure as hell sounded like family.
SemiJuggalo

@Background Pony #E7F7  
Actually, if you listen to how she sounds when she talks about how she hoped Sunset would return one day in search of guidance, she sounds genuinely concerned. Unlike in Legend of Korra, where Suyin had completely washed her hands of her former protege-turned-dictator, Kuvira. To be fair, Kuvira was not only mad with power, but she was also tearing Su’s family apart, after Su had finally gotten her older sister to stop hating her after 20 years.
Background Pony #50DD
@Background Pony #D2D3
 
I don’t think EG or the ‘fall of Sunset Shimmer’ comic support the ‘daughter’ angle. Celestia didn’t seem quite that close to her.
SemiJuggalo

@whitemew
 
@ThePonyBro  
Yep, the first EqG movie confirmed that Sunset made the decision to leave Equestria. Princess Celestia even said that she had hoped for Sunset to return one day, in case she needed guidance.
whitemew
Friendship, Art, and Magic (2018) - Celebrated Derpibooru's six year anniversary with friends.
Friendship, Art, and Magic (2017) - Celebrated Derpibooru's five year anniversary with friends.

riding the wind
@ThePonyBro  
Allowed back? she self exiled herself
ThePonyBro

God I want this to happen so bad…
 
I mean, sunsets good now right? By all rights she should be allowed to go back to equestria whenever she wants now, which means the reuniting could happen!
MrOwen

@Background Pony #D2D3
 
Sunset: Mommy, I’m sorry I ran away. Please, forgive me!  
Celestia: It’s okay, honey, dont cry. You’re home, and that’s all that matters.
Background Pony #84CE
headcanon: mother and daughter
Typewriterpony
Since the Beginning  -

Scholar of Golb
Celestia: “Don’t you fret, Sunset. Everyone gets dunked on at one point in their life.”  
Sunset: “B-but…IT’S JUST NOT FAIR!!”