Your example has the appositive NP as a supplement (as opposed to an integrated one). A supplementation consisting of one NP as anchor and another as supplement may have either multiple or singular marking.
John Smith's, my father's, car is red.
John Smith, my father's car is red.
The multiple-marking version is preferred in writing, probably because it allows the supplement to be set off by paired commas (or dashes). But it is the singular-marking version that is usually heard.
EDIT: The acceptability of the above examples is marginal. This is not because of doubts about the punctuation, but because the proper name should be the appositive element, not the head:
My father's, John Smith's, car is red.
My father, John Smith's car is red.