Two boys discover their teacher or principal is an alien and there is some plan that they must thwart. Their is a cave involved where the aliens are building or doing something that the boys must stop. I remember an illustration that the “principal looked normal except for a fairly large head or forehead. I remember one of the boys maybe having a sword that figured in the story.
Could it be the “My Teacher Flunked the Planet” series, by Bruce Coville? That does have three children, Peter, Duncan, and Susan, discover that their teacher, Mr. Smith, is scheming for an alien invasion of Earth. Together they manage to thwart his plans and get him to leave the planet; other books in the series deal with various other alien species and their curiosity about humans. Hope this helps.
This is my query. And by the way I do know the difference between “their” and “there”. That said, I can expand my description by saying the “aliens” in the school were like undercover agents. They could pass for human. I recall the setting to be a small or medium sized town. I read this in the early sixties. I remember it being one of my favorites. It would have been cataloged in either youth or juvenile.