After she quit her job, she accepted her defeat and returned to her parents' home.
「彼女は仕事を辞めた時、敗退を認めて実家へ帰った」は英語で「After she quit her job, she accepted her defeat and returned to her parents' home.」と言います。「敗北を認める」は英語で「accept one's defeat」と言います。
もう家賃が払えない…!と思った瞬間、彼女は敗退を認めて実家へ帰った。
The moment she realized she couldn't pay her rent anymore, she accepted her defeat and returned to her parents' home.