"The businesswoman is going on a business trip abroad for a week."
Translation:De zakenvrouw gaat een week op zakenreis naar het buitenland.
What is the problem with 'De zakenvrouw gaat op een zakenreis in het buitenland voor een week'?
Because you "gaat naar het buitenland" ("go abroad") or "bent in het buitenland" ("are abroad")
Okay, so how does it work if she is already abroad, and is going on a business trip while there? That is what I understood this sentence to imply...
I don't know if I completely understand what you mean but I'll try and be more specific!
"She is going abroad on a business trip" means "ze gaat op een zakenreis naar het buitenland"
"She going to study abroad" means "Zij gaatin het buitenland studeren"
it all depends on the verb -> "going abroad" is "gaan naar het buitenland" . And "are/going to ... abroad" is "zijn/gaan ... in het buitenland"
so "she is going to do business abroad" would be "zij gaat zaken doen in het buitenland" (cause of the verbs "going to do")
so if she was already abroad and going on a business trip while being there wouldnt the english sentence be "she is abroad and is going on a business trip" which would mean "zij is in het buitenland en gaat op zakenreis". Like I said I'm not completely sure I understand you question corectly so I hope this is more of a clarification!
You seem to have understood it well, that's a useful answer thanks. To me, the original sentence still leaves some ambiguity but I think the interpretation that she is not yet abroad, but will go abroad for the business trip is the better/ more common one.