How many people are in the picture described in this sentence? "I am looking at a photograph of Dominic and Rowan's mother."
It could be one or two.
Thanks to a reader for asking me this question. He correctly noted that the sentence is ambiguous, so congratulations to 30% of you. The photo could be of a man, Dominic, and a woman, Rowan's mother. Or, the photo could be of one person, a woman, who is the mother of both Dominic and Rowan. When you share the noun, you share the apostrophe, so if the woman is the mother of both boys/men, you need only one apostrophe.
To make certain this was not ambiguous, you would have to rewrite the sentence.