I have consulted a dictionary, but am unsure of the meaning of 关 in 休戚相关, 患难与共。
Also I'm not sure about the meaning of 与 in this context.
I get this answer from my Trusty translator. (Had to make her a coffee first!)
休：喜悦，吉利 happiness, luck
戚：忧愁悲哀 worry sadness
与共： have in common, we share
Edit: Found this link:
From an old song: Life's joys and life's miseries walk hand in hand and keep each other company.
Think that translates it nicely!