Iwanagahime no Mikoto is older sister of Konohanasakuyahime no mikoto(木花開耶姫命) who is enshrined at Mt. Fuji and also represent the god of Mt. Fuji.
In Japanese Myth, if you marry Princess Iwanaga who has an ugly out-look, you will have strong and long live children, and if you marry Princess Konohanasakuya who is very beautiful, all the children will have very short life like flowers. When Niniginomikoto (瓊瓊杵命) arrives Japan, he fall in love Princess Konohanasakuya in first sight. Her father let her and her sister, Princess Iwanaga, marry him, but because of Iwanaga’s look, he send her back to her father. After that, the relationship of the sisters is broken up.
Mt.Eboshi (烏帽子山) represents Princess Iwanaga, and Mt. Fuji represents Princess Konohanasakuya. Princess Iwanaga run away from Princess Konohanasakuya to Kumomi which has cloud always. When Mt. Eboshi is clear, Mt. Fuji get cloudy, and when Mt. Fuji is clear, Mt. Eboshi get cloudy. Also, legend said at the Mt. Eboshi, you cannot say good word to Mt. Fuji, otherwise, she will drop you off from the mountain.