Learn Russian: Он рассказал мне об отношениях со своей дочерью. - He told me about the relationship with his daughter.

Дочерью is the instrumental case of дочь, used here after the preposition со (with). Дочь is an irregular feminine noun. In all cases except the nominative and accusative singular, it adds the stem extension -ер- before the case ending. The instrumental ending for feminine nouns ending in a soft sign is -ью, giving us дочерью.

Why does the sentence use своей instead of его for "his"?

When the possessive word refers back to the subject of the sentence (here, Он), Russian requires the reflexive possessive pronoun свой (one's own). If you used его here, it would imply he was talking about some other man's daughter! Своей is in the instrumental case to agree with дочерью.

Why is the preposition со used instead of just с?

The preposition с (with) changes to со to make pronunciation easier when the next word starts with certain awkward consonant clusters, especially those beginning with с or з. Because своей starts with св-, the о is added to prevent the stuttering sound of "с-св".

The translation says "relationship" (singular), but отношениях is plural. Why?