The fallen attacked the reef and the queen spared the survivors. So yes they did betray her. Didn't you watch the cinematic?

The Eliksni, or "Fallen", lost the Traveler long ago, resulting in the Whirlwind, a catastrophic event that shattered their civilization. With the Great Machine gone they started to kling towards their Kells to lead them and the entire race (with the exception of House Judgment and maybe House Rain) became obsessed with power and leadership to the point of docking and Ciphers. I think that this obsession has resulted in them caring less for the source of power and more for the power itself. And the Queen is very powerful, and was a natural genius when it came to Fallen politics. She beat the others contending for House Wolves, and thus seized control. However, now Skolas rises, claiming to be Kell of Kells. This title was first mentioned in a prophecy from House Rain that also said that they would unite the fallen houses and reclaim the Great Machine. And with the fallen houses being so broken, and the Traveler so far from their reach, anyone who could do that would be absurdly powerful. And the Fallen respect power. Those that betrayed the Queen didn't do it out of loyalty to their previous Kell, but instead decided that Skolas is the more powerful and betraying her would be brownie points for them. Their was no indication that her Wolves would lash out against the Queen, and she honestly trusted her Fallen guards. She is probably the strongest person, or rather creature, in the star system that wouldn't destroy them on the spot. But the traitorous Wolves took a chance on prophecy that Skolas would be the Kell of Kells and be more powerful in the end.

Short answer? Shes cocky. Long answer? Ask me in the morning, im dreadfully tired.

“A side should always be taken, little light… even if it’s the wrong side.” She chose wrong.

She killed the House of Wolves Kell and apparently imprisoned all of the potential Kells in the Prison of Elders, including Skolas. Fallen don't rebel unless they have a leader of some sort. With no one to challenge the Queen, the House of Wolves was apparently content that she was their new Kell. Then the Nine requested Skolas for some reason. The relationship between the Queen, the Nine, Xur and their powers is pretty murky. but it appears that at least a portion of the Queen's power is based on something the Nine gave her. In exchange, she assists the Nine in their objectives, even if she doesn't entirely understand those objectives. So when the Nine requested Skolas, she gave Skolas to them. One of the Grimoire cards gives the interview Xur holds with Skolas after that. At the end, Xur frees Skolas and gives him a Ketch. I don't think the Queen knew the Nine (or Xur) would free Skolas. But once Skolas was free, he made the decision he needed the House of Wolves to help him become Kell of Kells. Hence, the betrayal. The queen didn't have knowledge that Skolas had been freed. she learned from the violence his freedom wrought inside her own kingdom as the Wolves escaped.

Wait wait wait if she killed the kell of the house of wolves and became ruler of that house shouldn't I be the kell of all the houses? I did kill skolas

She spared them and invited them into her peoples society most stayed loyal like house judgement and the house of crows only the house of wolves rebeled .

The entire reason the Wolves betrayed the Queen was cause of Skolas. If Skolas had never came back the Fallen would have never rebelled against her. She's basically the Wolves Kell and when there's an heir to the Kell throne (Skolas claiming to be Kell of Kells) it's all fair game.