The Carmelite Order traces its spiritual lineage all the way back to the prophet Elijah and the hermits who lived on Mt. Carmel for many centuries.
These hermits were reportedly present on Mt. Carmel during the lifetime of the Holy Family, and some medieval traditions claim that the Holy Family visited them on the way back from Egypt.
According to An Outline of Carmelite History published in 1926, Mt. Carmel was a place of pilgrimage for the Jewish people.
Carmel was a renowned place of pilgrimage for the pious Israelites and it is not at all unlikely that Mary, in the company of Joachim and Anne, whose home at Sephor, the capital of Galilee. was quite near, may have visited the Holy Mount as a child. It is also a tradition that the Holy Family stayed for a while there on their return from the Egyptian exile, taking up their dwelling in the School of the Prophets. This again is possible since Carmel lies on the direct route between Egypt and Nazareth.
While most modern historians classify this under the category of "legend," what is true is that the Carmelites were among the earliest religious orders to give honor to St. Joseph.
According to the Carmelite website, "The liturgical feast of the Saint Patriarch already appeared in the Carmelite Order in the second half of the XV century. In 1680 the General Chapter unanimously elected Saint Joseph as the principal protector of the Order."
Pope Benedict XIV claimed in the 18th century that, "It is to the honor of their Order that the Fathers of Carmel were the first to import from the East into the West the laudable practice of giving the fullest cultus to St. Joseph."
Throughout the history of the Carmelites, many saints were devoted to St. Joseph, such as St. Teresa of Avila.
While it may be a pious legend that St. Joseph visited the hermits on Mt. Carmel, the Carmelite Order has always been devoted to the Spouse of the Blessed Virgin Mary.