I have wanted to find this story for years as well because I read it in school in my English Lit. class and I even remembered that I had gone and looked for the novels at Borders but I had completely forgotten about it until today. So, to answer both of our questions, I did a little (extensive) research and this is what I found:
After searching a million key words to see if I could find it I decided to type "textbook" at the end of my phrase and one of the first sites that popped up was the Pearson - Prentice Hall textbooks site and looking at the covers I starting looking at the contests of each unit to see if something rang a bell and finally I read one that sounded right:
"The Threads of Time" by C.J. Cherryh in the 9th edition of the Grade 10 textbook under Unit 2: Short Stories, it's the very first story in the list.
So I went ahead and googled it (it was like my 40th google search on a title) I found this in wikipedia:
The Collected Short Fiction of C. J. Cherryh is a collection of science fiction and fantasy short stories, novelettes and novella written by the United States author C. J. Cherryh between 1977 and 2004. his collection is divided into three sections: Sunfall (stories from Cherryh's Sunfall collection plus a new story, "MasKs"), Visible Light (stories from Cherryh's Visible Light collection) and Other Stories (stories from other collections and magazines).
- "Frontpiece" (Visible Light, C. J. Cherryh, 1986)
- "Cassandra" – short story (The Magazine of Fantasy & Science Fiction, October 1978)
- "Threads of Time" – short story (Darkover Grand Council Program Book IV, 1981)
- "Companions" – novella (John W. Campbell Memorial Awards Vol V, ed. George R. R. Martin, 1984)
- "A Thief in Korianth" – novelette (Flashing Swords! No 5: Demons and Daggers, ed. Lin Carter, 1981)
- "The Last Tower" – short story (Sorcerer’s Apprentice, Winter 1982)
- "The Brothers" – novella (Visible Light, C. J. Cherryh, 1986)
- "Endpiece" (Visible Light, C. J. Cherryh, 1986)
- Alien Stars (Baen Books, 1985), a book of Military science fiction, includes Cherryh's Hugo-nominated novella "The Scapegoat"
And then, reading farther ahead I saw this:
"The Threads of Time" revisits the Gates in Cherryh's 1976 novel Gate of Ivrel.
Which led me to search the novel "Gate of Ivrel" and found this (which I had previously seen but thought it was incorrect) in wikipedia:
Gate of Ivrel is a 1976 science fiction novel written by C. J. Cherryh and was her first published work. It is the first of four books composing the Morgaine Stories, chronicling the deeds of Morgaine, a woman consumed by a mission of the utmost importance, and her chance-met companion, Nhi Vanye i Chya. It is tenuously set in her Union-Alliance universe, but has little in common with other works in that milieu.
And THEN, looking into the "Morgaine Series" I found this in wikipedia:
The Morgaine Stories, also known as The Morgaine Cycle, are a series of science fantasy novels by science fiction and fantasy writer C. J. Cherryh, published by DAW Books. They concern a time-traveling heroine, Morgaine, and her loyal companion Nhi Vanye i Chya.
The first book in the series, Gate of Ivrel (1976), was Cherryh's first published novel, and was followed soon thereafter by Well of Shiuan (1978) and Fires of Azeroth (1979). These three works have been subsequently released in omnibus editions under various titles, including The Book of Morgaine, The Chronicles of Morgaine, and The Morgaine Saga. In 1988, Cherryh published the fourth book in the series, Exile's Gate.
This series has been identified as being set in the Alliance-Union universe, as it is stated that Morgaine was sent on her quest by the "Union Science Bureau".
The construct at the center of these novels is a set of "gates" that facilitate travel among a series of distant worlds connected by these gates. In addition to traveling from place to place, the gates can also be used to facilitate time travel.
Because of the temporal paradoxes involved in time travel, the gates are a threat to universal causality and therefore to the future of innumerable worlds. In fact, as presented in the backstory of the Cycle, unwise use of the gates' temporal properties has already decimated at least one highly advanced civilization, the qhal. To prevent additional such calamities, Morgaine is engaged on a centuries-long (and potentially infinite) quest that takes her from world to world via the gates, setting each gate to self-destruct just after she has used it to move on to the next.
I hope this tiny little research helped you find what you were looking for. Just in case, I also found this page where someone sort of summarizes and analyzes the short story.