Is this the correct use of an apostrophe when showing a name and relationship?
When was your father, Robert's, wedding?
I'm not sure there is a way to correctly render it using an appositive and an apostrophe. Instead, if you want to keep representing the possessive with an apostrophe, I'd make "Robert" an essential clause and remove the comma altogether:
When was your father Robert's wedding?
Since one can assume there is no ambiguity about 'your' father's name, wouldn't the sentence perhaps sounds better as just:
'When was your father's wedding?'