He went with her to both her urologist and gynecologist appointments
chaperoneは聞いた限りでは、大人・未成年の関係で連れ添う場合で使いますので、he went with her as a chaperoneを言うと、お父さんと娘さんを想像します。
例えば、
Her parents chaperoned at the elementary school field trip
Her parents were chaperones at the elementary school field trip
彼女の両親が小学校の遠足に連れ添った
恋愛関係であれば、He went with her to both her urologist and gynecologist appointmentsの方が自然な表現ですね。
went with=連れ添った
accompanied her to~もOKですね。
ご参考になれば幸いです。