Originally Posted by zresnik
Just so you know, Webster's definition of deportation is "the removal from a country of an alien whose presence is unlawful or prejudicial," which is exactly what the case was. We didn't have proper documentation, so we were deported. So don't try to impress anyone else reading the forums, and don't try to sound superior by getting clever with me, when you are ultimately wrong.
Let me be clear with you, once and for all. I know quite a bit more about this than you do, and I'm not going to argue with you, except now. You were not "deported". You never entered or were admitted to the country. You weren't removed from Costa Rica, you were turned away from Costa Rica. The fact is that if you intend to enter Costa Rica again for your vacation, and Costa Rica is not objecting, then you weren't deported. People who get deported usually don't just up and legally re-enter a country from which they have just been deported.
Now, it sounds to me like AA made an error allowing your family to get on at LGA. And as you mention, they will be fined. I am very surprised something like this was not caught by AA in LGA, and so they made you fly all the way there so you could get bounced back, as opposed to getting turned away in LGA. If it was indeed, their fault, then I assume you'll get something for your troubles of having to fly all the way there and back for no reason. At least, I'd like the flown miles...