Next to me, my wife — with whom I'm in the middle of a fight — is sleeping.

Literal

Beside [at-に][topic-は] fighting-state [possessive-の] wife [subject-が] sleeping.

喧嘩状態の妻 'wife in a fighting state' — a compact relative clause. 横には 'beside (me)' uses に for location + は for topic. 眠っている 'is sleeping.' The juxtaposition of marital conflict and peaceful sleeping creates a wry, relatable domestic scene.