I am unable to locate objects and their orientation with respect to myself when 向こう and 向かい are used.
Consider:
向こう側
向かい側
向こうの店
向かいの店
Where is 向こう側 and 向かい側 with respect to me? Are they the same place?
My current hypothesis is that 向こう and 向かい both may occupy the same place, except that 向かい necessarily orientates the object to face the subject (either the first person, or from some place's perspective which the first person adopts) by either the having a "front side" or by assuming that the object has a "front side".