I ran into this as well when writing my fan fiction. I made it so Shadowheart wasn't in the party and Lae'zel revealed to him that Shadowheart had the weapon and where she was. So he jumped on Qudenos' back to go after Shadowheart while Baretha and her party attacked Lae'zel and company. That, at least, made more sense. I even had the Kith'rak tell Baretha that if Lae'zel and company actually did wind up having the weapon, she was to give it to him and NOT return it herself. He was NOT about to let anyone but himself claim that prize for his queen.

That makes way more sense than what is currently there.

I also came up with another scenario that could potentially work. To save the party, who are the Absolute's Chosen, suddenly, at the end of the scene as the Kith'rak is about to kill Lae'zel and company, goblins and drow IN MASS NUMBERS, ambush the Githyanki, coming out of the mountain pass. While Kith'rak and dragon fight off the horde, the Kith'rak leaves Baretha and company to kill Lae'zel and party. Yeah, Dragon Fear would crush goblin spirits, etc., unless the Absolute was empowering them to resist; doing what they can to throw their lives away to save the Absolute's Chosen.

Anyway, something like that is really needed in this scene. I love having the dragon show up and the Kith'rak there and so forth, but there needs to be a much better reason for them leaving. Shoot! Even a Mind Flayer ship dropping out of the sky suddenly to try to seize the weapon would draw the dragon and rider away and make sense with the story. Anything but, "I have to go report back to base now that our mission is complete even though I could kill them first and then take it myself back and present it myself and gain all the honor for myself."