Perhaps "A Swiftly Tilting Planet" by Madeleine L'Engle?
Charles Wallace is traveling in time with a unicorn, named Gaudior, to try to save the world from a mad dictator who is close to starting a nuclear war. At each point in time where he stops, he gets somehow put into a person in that time, living that person's life but able to somehow influence things. It was called being sent "Within".
His married sister, Meg, follows him telepathically. They call it "kything". She does it sitting in her bed with a dog and a kitten, and it works better when she is touching the dog.
Does "St. Patrick's Rune" ring a bell? Charles Wallace recited it at many points during his journey, usually when in some kind of trouble. It had some power. I believe he had learned it from Meg's somewhat mad mother-in-law. It starts, "At Tara in this fateful hour,
I place all Heaven with its power,
And the sun with its brightness,
And the snow with its whiteness," Etc.
"At Tara" is sometimes replaced by "With Gaudior"
This is the third book in a series, but each book stands alone also.
The book is available on Open Library https://openlibrary.org/