If you need that character’s perspective to tell the story, then by all means include it. However, springing the second character’s perspective on the reader at the end can feel abrupt, as your readers have mentioned. Even worse, it can feel like trickery on the author’s part.
We all know the opening of a story should establish conflict, introduce character, and create a sense of place. But it also achieves a subtler—but no less important—task, whether the writer is aware of it or not: establishing a point of view strategy. In the opening of a short story, you are letting the reader know who is telling the story and the limitations of that storyteller. Readers create expectations based on this information and this establishes a contract, one that readers probably aren’t even aware of. But breaking that contract can make for an unpleasant reading experience. While you don’t have to stick to one character’s perspective, you should indicate your intentions in those early pages when that contract is being solidified.
One approach you might try is to go back and forth between the two characters’ perspectives, staying in one perspective for a chunk of time, then shifting to another for some time, and then shifting back. This will introduce the second perspective earlier and let it appear throughout. Hannah Tinti uses this technique—integrating several characters’ perspectives—in her short story “Home Sweet Home.”
This would prepare the reader for the shift you make late in the story. You may even create tension in the process, as the reader wonders what role the second character’s perspective will play in the unfolding story.
That being said, you may want to create a jarring effect at the end, and using perspective shifts can achieve that. In Anton Chekhov’s short story “A Trifle From Life,” Belyaev goes to see Olga, the woman with whom he’s having a romance. She is not at home and he talks with her young boy, Alyosha, while he waits. During their conversation, Balyaev learns Alyosha and his sister have been seeing their father in secret and this upsets him. The story focuses mostly on Balyaev’s perspective, though there are brief moments of Alyosha’s. Then, at the very end of the story, when Belyaev reveals this secret to Olga, we suddenly zoom in very close on Alyosha’s perspective:
And Alyosha sat down in the corner and told Sonia with horror how he had been deceived. He was trembling, stammering, and crying. It was the first time in his life that he had been brought into such coarse contact with lying; till then he had not known that there are in the world, besides sweet pears, pies, and expensive watches, a great many things for which the language of children has no expression.
The focus on Balyaev’s perspective for most of the story lulls the reader into thinking the story is about his distress of learning about the father’s presence in the children’s lives. The intentionally jarring shift of focus at the end, however, reveals the story is really about the boy’s experience of betrayal.