After he had an argument with his girlfriend, and things had settled down, he went to her house to apologize.
この場合、次のような言い方ができますよ。
ーAfter he had an argument with his girlfriend, and things had settled down, he went to her house to apologize.
「彼は彼女と口論し、落ち着いた後、謝るために彼女の家に行った」
to have an argument with ... で「…と口論する」
to settle down で「穏やかになる・落ち着く」
ご参考まで!