Showing Storm at the Edge of Time by Pamela F. Service

Suddenly, a visit to an ancient stone circle whisks her back into the past. She has been summoned, along with Arni, a boy from Viking times, and Tyaak, a half-alien boy from the 26th century, to search the past, present, and future for three broken sections of a magical wooden staff. As the trio experience each other's worlds, they find deeper mysteries to probe and problems to solve, which could affect the entire time line of the planet.