On the desk, there was a framed photo of a child and a wedding photo.

Literal

Desk [on-の上に] picture-frame [in-に] entered child [possessive-の] photo [and-と] wedding [possessive-の] photo [subject-が] existed.

A descriptive sentence with layered pre-nominal modification: 写真立てに入った modifies 子どもの写真, creating a nested relative clause. Note how Japanese stacks modifiers before the noun — 'frame-in-entered child's photo' — where English needs a postposed 'photo of a child in a frame.' The existential あった sets a past scene, common in narration.