People who overreact to superficial matters should not be in positions of managing others.
Literal
Superficial things [to-に] overjoyed-and-depressed person [subject-が] person [object-を] managing position [to-に] stand [should-not-べきではない].
一喜一憂する is a 四字熟語 meaning 'to alternate between joy and sorrow, to overreact emotionally.' 管理する立場につく means 'to take a position of managing.' べきではない expresses 'should not.'