Why is it 出差去 and not 去出差?
adding some thoughts here as a native speaker:


You can say 前几天爸妈去出差了。There's no semantic difference to me in this case.
Under the hood, the syntax are different. In 去出差, 去 indeed means "to go", and the phrase's nothing more complicated than the literal translation you've mentioned: "go on a business trip". 
But in 出差去, it's the 出差 that's the verb. 去 following verbs, just adds the feeling of "already gone". For example, 他吃晚饭了 means he's had dinner, while 他吃晚饭去了 means he's left for dinner.
出差 business trip itself already carries the meaning of gone/left. Therefore in this case, it actually doesn't make a big difference with or without 去 in the end.
Just like "go" in English, 去 sometimes can be tricky in terms of pragmatics. In user3306356's example 咱们看电影去。 看电影去 has a more cheerful, friendly tone compared to 咱们去看电影。In fact, the 去 + verb sounds so decisive that I rarely hear people use it without adding a 吧 in the end to soften the tone, when proposing an idea in daily communication.