They cure Kerrigan at the end of WoL right. At the start of HotS, they get attacked by Dominion, Raynor comes to pick up Kerrigan but they have to go separate ways when a bridge explodes(...). Raynor gets killed by Nova(lololol it's Nova from the game that was never released so funny and cool). Kerrigan goes berzerk when she thinks Raynor is dead and assume control of the swarm again. Recruits an army and kicks Dominion out of Charr again. Zeratul comes in for no specific reason, tells Kerrigan about the planet the Zerg originated from. She goes there, bathes in the first spawning pool, becomes an even stronger version of the Queen of Blades and reverts to old form. Also allies with Primal zergs which are zergs that don't rely on the Hivemind connection. At this point they hear that Raynor is actually not dead, Mengsk captured him and is trying to blackmail Kerrigan into not attacking since she was going to rape his ass. She decides to rescue Raynor first, run into the main disciple of Amon the guy who created the Swarm as a weapon and shit, tie in for the next game. She rescues Raynor, but Raynor isn't happy cause she all ugly again, but when she attacks Mengsk capital Raynor joins her cause yay good ole times let's fuck shit up. Kill Mengsk, kiss goodbye to each other, the end.
The only important parts so far of the story is that in WoL they cure her so even though she's back to Zerg queen again, she now has full control of her thoughts instead of being under the "curse of Amon" or whatever. Then the 2nd important part is that they killed Mengsk, so Valerian will become emperor or whatever. The only stuff that remains is the Amon plot thing with hybrid zerg/protoss shit and the final war, which will probably see an alliance of Raynor and Kerrigan to help to protoss fight that shit off against a 4th enemy instead of each other like it should be.