In Dragonlance "the heroes" part, 5 years pass and all of the sudden Kitara is the overlord of the blue Dragon army. Are there any books detailing this or did it just happen behind the scenes?
Mostly behind the scenes
There is no direct full story in any Weis/Hickman book (which form the canon). Some books by other authors may shed a light on it, but most of them may contradict the canon. Probably another book was planned, but since Weis and Hickman, who authored Kitiara, along with all other Heroes of the Lance, finally parted ways with the Dragonlance world owners (Wizards Of The Coast, Inc, owned by Hasbro, Inc) around 2004, there were no more books on Kitiara.
The only canon books to partially tell the story are:
Brothers In Arms (sequel to The Soulforged), describes the beginning of Kitiara's rise to command, along with the Twins' adventures as mercenaries. But the story ends when she is still far from high command.
Dragons of the Highlord Skies tells how Kitiara won the favor of Lord Soth and settled in the Dargaard keep, thus becoming second to Ariakas only.