Great movie. I wouldn't have had it any other way. But, for purely academic reasons, let's debate the questions in this movie. There are plenty, but I will ask just one, and let others provide answers and ask questions of their own.
So, my first question is:
1. Why didn't the mother explain to the boys where he had been before entrusting them to him?
IMDB has for some reason performed a forum "bloodbath" of posts on this film, many of which addressed your question. One possible explanation for the mother's actions is that the "father" isn't the boy's father. The events of the film's opening--Ivan's fear on the tower, the mother having to save him, the "miraculous" return of the father--suggest to me that the woman got a friend or distant relative who resembled the father (or even hired someone) to take the boys for a "man-up" trip. She arranged the whole thing, and the impersonator decided to kill two birds with one stone, go to the island...and things spiraled downward, so to speak, from there.
shareIt doesn't seem like it would be appropriate to explain that before the trip. Obviously she didn't tell them all the years before, so it was clear to them that she wasn't comfortable talking about it. The trip was probably the perfect time for him to explain that himself.
The impersonator theory seems very far-fetched to me, and it would pretty much defeat the entire emotional purpose of the movie.
I have a couple questions. First is, of course, what's in the box, which isn't that important anyway but should have still been explained a little. I'm not asking for it to show us exactly what's in it, but at least some evidence to help us decide would be nice. I don't think this question is possible to answer really, and probably wasn't intended to be or else the movie would make a bigger deal of it.
The other question is where was the father all those years and what was the job he was doing? To me it seems like he was definitely a criminal of some kind. I think there was a scene of him carrying what looked like a dead body, right? And just his overall shadiness and peculiar details of his job should be screaming to you that it's something illegal. It seems pretty clear that he was on an island somewhere, because he was tired of eating fish. That suggests that he was either on the island they were going to, or maybe in prison on a different island.
Also the pictures at the end are a little confusing. Some are from the trip, but a lot of them are clearly much older. I'm not sure if the movie was just showing us some family history, or if all of these pictures were supposed have been together somewhere.
The impersonator theory seems very far-fetched to me, and it would pretty much defeat the entire emotional purpose of the movie.
The first scene where he was being bullied was part of the plot. It all played into how the characters acted for the rest of the movie, and the death scene which was obviously directly related to the beginning scene. It doesn't imply some hidden part of the story.
The phone call seemed to just be implying that he was involved in some shady stuff. That scene and him calling off the trip later is just more evidence of his past, probably as a criminal. I don't know why you're reading into stuff that's much more likely to just be plot devices.
Also as I said earlier, what would be the purpose of the movie if that was true? It was carefully written as an emotional movie. The whole point of it was seeing the father and the kids interact, how the kids feel about him, his attempts to figure out how to act with them now, his death, the kids having to drag their own father across the island, etc. But you're saying that the movie was actually a story about a kid being tricked into "manning up" over the weekend? I don't think so.
While I did not personally see the whole film but just the second half, I never found myself doubting the father's parenthood, and none of the pages I have taken a look at on Wikipedia insinuate otherwise, either: http://en.wikipedia.org/wiki/The_Return_%282003_film%29
However, to play with the idea, I think the fact that he emotionally screamed "Ivan, my son!" just before he fell, is proof enough för him indeed being their father, as he at that very moment had lost all his emotional bounds, and it is known that a person that do so, generally also lose their ability to lie and hide the truth.
It is also questionable whether he had seen any reason at all to try to save the darn brat - that was after all the cause for much of the spiraling negativity, refusing to obay the fathers conditions, finally ending up with them in the high air - had Ivan just been a random kid that he had no relation to. Yet, the father cared very much trying to save Ivan.
In the end, I actually found it extremely difficult to fully sympathize with Ivan, and instead found myself rooting more for the father.
All in all, a terrible and depressing movie, but that is what is in fashion nowadays.