。
Please try stopping by again next Monday.
Literal
Next-week [possessive-の] Monday [on-に] once-more honorific-stop-by [try-みて] please.
お寄りになる is the honorific form of 寄る ('stop by'), built as お + masu-stem + になる. Combined with ~てみる ('try doing') and ~てください, the whole sentence is: 'try stopping by honorably again.' Heavy keigo stacking for polite recommendation.