It may have migrated that way to Amrikay, but the Irish original had this as the next verse:
"I'm sorry, my neighbours, I married this young one! She favours the neighbors and none of her own! She goes out all night, out to balls and to parties, And leaves me here rocking the cradle alone!!
Which seems to indicate it a marital problem rather than a chattel arrangement. Although, I suppose, the two might sometimes be similar....