。
She listens to her son with a generous, patient ear.
Literal
She [topic-は] generously son [possessive-の] talk [object-を] listens.
寛大に is the adverbial form of the na-adjective 寛大 ('magnanimous, lenient, broad-minded') — the kanji literally 'broad-big,' painting tolerance as spaciousness of mind. The pattern is the regular na-adjective + に for adverbial use. 話を聞く is the everyday phrase for 'listen to someone's story / what they have to say,' broader than English 'listen' because 話 ('talk / story / matter') can refer to anything from gossip to a confession. The non-past 聞く (rather than 聞いている) here reads as habitual: this is what she generally does, not what she's doing right now. The sentence has a slightly approving tone, framing her listening as a virtue rather than a chore.