possessives - Is it "John or Mary's house" or "John's or Mary's house"?

I understand that if John and Mary own a house together, it is John and Mary's house. If they jointly owned multiple houses, they would be John and Mary's houses. I also understand that if John and Mary each own one or more houses, then one would refer to John's and Mary's houses. However, what if John OR Mary own a single house. Would that be John or Mary's house or would it instead be John's or Mary's house?

To take this a little further, substitute for John and Mary an individual person who might be an owner or a renter of a single house. You don't know or care if the house is in the possession of an owner or of a renter but you want to convey that the person might be either an owner or a renter. Would one refer to the owner or renter's house or to the owner['s] or renter's house?

In real life, I'm looking into "the Social Worker['s] or Attorney's employee identification card." A form must be accompanied by a copy of the employee identification card of the person submitting the form. The form could be submitted by the Social Worker or by the Attorney.

I'm also looking into "the child['s?] or youth's birth certificate." The birth certificate belongs to (is that of) a person who might be a child or a youth. (There is no single word we use at my job that refers to young minors and to older minors collectively).

There's the possibility of my restructuring or 'pluralizing' the sentences to convey the intended meaning but it'd be best if I don't.

A million and one thanks all.