The mine that Oliver Cowdery initially wrote in 𝓟 (“mine younger brethren”) was a simple scribal error influenced by the preceding “and Sam mine elder brother and his family”. Oliver quickly corrected his error (the level of ink flow is unchanged). In the Book of Mormon text, when mine occurs attributively in a noun phrase, the following word (whether adjective or noun) is always vowel-initial or h-initial. (The initial h was often silent in the language of the King James Bible, which means that originally in Early Modern English the attributive mine occurred only when the following word began with a vowel.) For further discussion regarding mine versus my (and thine versus thy), see possessive pronouns in volume 3.
Summary: Maintain the use of my before younger in “my younger brethren”; in attributive position, mine can occur only when the following word begins with a vowel or an originally silent h.