Found something that may explain this. In the Books of Sorrow, the cost of Savathun’s worm is that she “must never abandon cunning.” Perhaps the worm curse takes priority over the sisters’ bond, leading her to betray Oryx?
In the Books of Sorrow, the Osmium Siblings are near constantly “betraying” each other. They need to, because that is how they grow in power:
BETRAYAL. We have marooned Oryx within the Deep. This is our obligation as lords of the Hive, to make war upon each other, to eradicate weakness and make ourselves sharp.
It’s not just Savathun that must constantly feed her worm; Xivu Arath and Oryx took the same oath. Yul specifies this when the sisters make the bargain:
You must obey your nature forever. In your immortality, Aurash, you may never cease to explore and inquire, for the sake of your children. In your immortality, Xi Ro, you may never cease to test your strength. In your immortality, Sathona, you may never abandon cunning.
The Hive do not see this as ‘betrayal’ in the same sense as we would think, because to them love and war are the same. The sisters killed each other hundreds of times, plotted against each other; Oryx at one point destroyed Savathun’s warship and part of her Court. And, as cunning as she is, there is little in the Books to point towards her actively attempting to take Oryx’s crown. She is the one that suggests they separate:
Then sayeth Savathûn, “Siblings, listen, we must part ways a while, so that we may grow different.” She flies her war-moons into the black hole. Her throne becomes distant.
And she is also wary of the Taken power:
Savathûn asks if I am as much a slave of the Deep as my Taken. She asks what price I pay for my power.
I do still think she’s in charge of the Taken, especially given the wealth of evidence in D2. However, I don’t think her worm is the reason for her takeover. As Red has pointed out, Dreadfang is probably written from the perspective of Savathun:
Kingly brother, I thank thee for the gift of thy failure. The sword logic demands a pinnacle.
This implies that Oryx failed, not that Savathun undermined him. It’s not off the table, especially since the Books aren’t nearly objective, but Savathun might just be seizing the opportunity.
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And if you focus on the main missions ( those with a blue crown symbol ) given to you on Io,you’ll eventually fight a manifestation of Quria - Blade Transform.
Yes who was given to Savûthun as a gift by Oryx after he was taken. But does this imply that she controlled Quria like Oryx controlled the rest of the Taken. And if so could she possibly use that control to establish herself as the taken king?Just throwing it out there 
Quria is different from the rest of the Taken in that it still has some will. Oryx says this in XLIV:
“Quria contains a Vex attempt to simulate me. It might generate others — you, perhaps, or Xivu Arath. I’ve left it some will of its own, so it can surprise you.”
Savathûn having Quria doesn’t automatically grant her the ability to control the Taken; if it did, Oryx probably wouldn’t have gifted it to her.
Having Quria probably isn’t hurting Savathûn’s plans (if it is her, which is looking more and more likely). However, having control over the Deep, and by extension having the power to Take, requires the Tablets of Ruin:
Auryx the First Navigator set upon his god with his sword and his words, and cut Akka to pieces, and took from those pieces the secret of calling upon the Deep. He wrote this secret on a set of tablets, which he called the Tablets of Ruin. And he wore them about his waist.
Oryx being dead means no one currently has the Tablets, and Savathûn could have very well taken them from the Dreadnaught and restarted Taken operations- and, looking at the fact that some Red Legion forces have been Taken, it appears that someone has been using them. But Quria isn’t the pathway Savathûn would take to take her brother’s mantle.
I suppose so. 
I’ve been brainstorming A LOT on the destiny lore. Eris and Savathûn must be connected in some way. Savathûn has wanted the power to take. She tried to kill Oryx by tricking Crota into opening his realm to the Vex, that failed. Even after that she still planned to attack his vulnerable realm, but Oryx built the dreadnaught. She knows she can’t stop, her worm must feed from her cunning or else she will die. She can’t kill Oryx head on, it’s too obvious. We don’t know exactly what happened in the Hellmouth when Eris was down there, I believe Eris and Savathûn made a bargain. How else could have Eris survived that long without a Ghost? Savathûn gave her a worm, it makes sense, why else would eris have the eyes of the hive? Eris is now an agent of savathûn. So savathûn sends eris to get the aid of the guardians to kill crota (who happens to be the heir to the Osmium Throne), which draws out oryx. Once again we become agents of Eris, agents of savathûn. Now the seat of the throne is empty, and savathûn sits in it. Some game of thrones stuff going on.
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