。
Yuriko thoroughly enjoyed their rare tryst to her heart's content.
Literal
Yuriko [topic-は] occasional tryst [object-を] heart-going [until-まで] enjoyed [regrettably-てしまいました].
逢瀬 (おうせ, 'tryst, lovers' meeting') is a literary/romantic word. たまの ('occasional, rare') emphasizes how precious these meetings are. 心行くまで ('until the heart goes' = 'to one's heart's content') is a literary idiom. ~てしまいました here conveys not regret but completeness — she indulged fully. The whole sentence has a romantic-novel register.