Well the elephant in the room is....they should have gone down there....

***spoilers***

....right away, and bribed her way out. I repeat, the family should have gone down to Ecuador right away, and they should have brought cash (or wired it) and bribed her out. This is what the police are expecting. This is why people are held without trial. It's expected that the family (or associate) of an American come down there and bribe them out.

Instead, the daughter waited 6 months before even setting foot in Ecuador. Making phone calls and sending stuff and trying to do things the 'legal' way is a gigantic waste of time. It's possible that a naïve middle-class American family would not know this. They might make mistakes and waste time. They might try the legal way. But I think most people know by now (due to the internet, etc. - I think this incident occurred before the internet was so popular) that the way to go is to get your @ss down there and grease some palms. Man they wasted a lot of time doing it the legal way.

Not that I blame them. They just didn't know better.

Plus it would be a boring movie if they got her out in a month lol.