The Time Keeper (Timeways Book 1) (The Timeways Trilogy)

From School Library Journal (refers to print edition)
GR 6-10
A light, fast-paced and readable adventure that combines elements of romance, science fiction and fantasy. Jeanette Lacy, an unhappy 15 year old, attempts to find her runaway brother Neil and ends up being transported to another time. The time-transport stones are located in an old hotel scheduled to be destroyed in a few days, so the plot-clock starts ticking as Jeanette and Neil wander thorugh different centures, not always on Earth, before reaching home. Reviewer Yvonne A. Frey, Peoria Public Library, Illinois.

The glowing stones seemed to throb with some unknown power. What were these stones and why were they here in this hidden cavern? All fifteen-year-old Jeanette Lacy and her younger brother Neil knew was that the stones were calling to them. . .and they couldn't resist.
But their first steps on this weird pathway took them whirling through time to Texas--one hundred and thirty years ago in another past. Texas, where two moons hung in the sky, where unicorns were only too real, and where a boy named Jesse became an unexpected ally in their quest to return home. Then, instead of home, the stones sent them off to a frightening future where traveling in time was the worst crime of all. Originally pulished in 1985 by New American Library and Dragon Books (United Kingdom).