It's honestly pretty simple. Technically, her family did find out the Amulet of Avalor had magical properties as they were informed Princess Elena was trapped in there in that 3 parter of season 3. However, they obviously don't know the full extent of the Amulet's abilities like being able to control size, transfiguration, making a laser pointer out of the shine and of course, speaking to her animals. Of course, Amber is the exception. She's the only one known to know about Sofia's amulet's true power, the Secret Library, the Mystic Isles and the duty of Storykeeper. James had went on an adventure with Sofia to help the dragons, but was completely oblivious to why Sofia was there. Anyway, I'm rambling. Sofia has been known to be very secretive about how powerful her Amulet truly is and her job as Storykeeper, her big heart is her stregnth and weakness. She wants to protect her family. If any evil doers were to find out the Royal Family's youngest child had one of the most powerful magical objects in the world, they'd certainly use it to their advantage, similar in Infinity War. "I'll give you your family back IF you give me your amulet" type of thing. They're just better off not knowing imo.