I was prepping an analyst post when I came across this thread. I'll try my best to answer it as it appears to me. For these to make sense I will see "Varus" as the Darkin. Kai and Valmar are separate entities from "Varus" within the body.
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Varus is in control, primarily anyways. All three are united in a series of goals in a passive sense, however it is the Darkin who controls the body mainly. Val and Kai come along for the ride in the hopes that they'll be separated from Varus once more. I'd say that Kai & Valmar have control do some degree, depending on what is happening at the given time for them to try and reign in Varus, before the Darkin takes over again.
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Control swapping appears to be dependent on what may cause Kai & Valmar to resist Varus, and it seems to heavily spurred by emotional experiences. In the Heartlight comics, Valmar's mother allowed Valmar to come to his senses and prevent himself being absorbed completely into Varus. In the Dark Kin flavor story, Valmar resisted Varus initially when he went to slaughter the main armed guards. He reneged on killing the laborers because spilling innocent blood seems to be what tips the balance in Kai & Val's favor due to their raw emotion destabilizing the control of Varus' body.
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Resisting has only been shown to us a little bit. However as I highlighted above, strong and raw emotional responses are what seem to be the core functionality of allowing the two hunters to resist the Darkin. Kai & Valmar's love for each other ended up being the strongest emotion, overwhelming Varus' hate for the destruction of the Darkin race. Valmar recognizing his mother's voice was another one, because as they are merged entities, it is highly likely that Varus has memories of Kai & Val's life experiences due to him also recognizing Valmars' mother. A third case is when Varus went to slaughter the armed guards in the short story. Valmars' initial resistance caused Varus to be spotted, his surprise attack being ruined and forcing him to fight.
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Confirmed as Varus in the comics. No double letters it appears.