she went out after she had finished the housework

我觉得第二句应该是she went out after she finished the housework.

意思大致相同。
只是前者强调出去之前“已经完成功课了”；后者语气平些：仅仅译成做完功课出去。

个人觉得好象第二个错了....
after后面要接时间吧....

She had finished the housework before she went out
她在出去之前就完成作业了。强调写完作业

she went out after she had finished the housework
她写完作业后出去了。强调出去的动作