"My mom is going to ask for leave next week."
下个星期我的妈妈会请假 (xià gè xīngqí NOT shàng gè xīngqí) was accepted.
上个星期 means LAST week.
I don't see why I cannot say, "Next week, my mom..." instead of "My mom, next week..."
Shouldn't "ask" for time off and "take" time off translate to different phrases?
Is the Chinese saying "next week, my mother will ask for leave (to be taken at some unspecified time)"? Would changing the word order to 我的妈妈会请假下个星期。change the sense to "my mother is going to ask for leave, which will be taken next week"? Or is this word order even possible in Chinese? If not, how would the latter be expressed? Is the given phrasing ambiguous, as it is in English?
我的妈妈会请假下个星期 is not correct. 下个星期我的妈妈会请假 is.
To more clearly mean the request will be forwarded next week, you can say 去+请假, e.g. 我的妈妈下个星期会[去]请假.
Also see my reply to DieFlabbergast.