Ellen Q. answered 07/07/21
College and High School Chinese for Classes and Tests (AP& IB)
The answer is no.
V+来\去 is the simple complement of direction. If the object of a sentence is a word denoting the place, it is placed after the verb and before ‘ 来\去’, eg
他下楼去了。He went downstairs.
我们进教室去吧。Let's go to the classroom.
她下周回学校来。She will come back to school next week.
你应该上山顶来看看风景。You should come to the top of the mountain to see the scenery.
他们要到中国去旅游。They are going on a trip to China.
Since 家乡 is a place, so the right way is 回家乡去,not 回去家乡。When the speaker and the listener both know the location in the conversation, the location could be omitted in most cases.
If the object of a sentence is a word referring to something, it can be placed before or after '来\去', eg
He brought a book. 他带来了一本书。
他带了一本书来。
Friend sent me a message. 朋友给我发来了一个短信。
朋友给我发了一个短信来。