My father looked at my mother with a dazzled, admiring gaze.
Literal
Father [topic-は] dazzled-seeming mother [object-を] looked-at.
まぶしい means 'dazzling/blinding,' but まぶしそうに goes beyond literal brightness — it suggests looking at someone with admiration or being struck by their radiance. ~そうに is the adverbial form of ~そう (appearance-based), modifying the verb 見る. A tender, literary image.