Let’s review.  Apostrophes are used to show possession.  (They are also used for contractions, but that is another lesson).  This implies that something is possessed.  Hence, you would expect to find an object following an apostrophe.  If you insist on signing your Christmas card, “The Peterson’s”  I will be forced to pencil in my own object of choice, and believe me, you won’t come off well.    The Peterson’s what?  You must be trying to tell me someone/something too unmentionable to name is authoring your card.  My edit will not be so favorable as to be “The Peterson’s Cat.”  It will more likely be “The Peterson’s Bunion” or “The Peterson’s Irritable Bowel.”   Possibly, “The Peterson’s Undead Zombie Barista.”  So save yourself the derision and apostrophize correctly.  It is my one heart’s (see that?) desire.