The problem is that you only have a thousad words to work with, and knowing when to cut the crap is more of an art than a science. In all honesty, I'd be hard-pressed to write your story in 2500 words. It doesn't help that you have a due date for the assessment either.
The first thing I'd kill is two of the brothers. Don't even both putting them into the story because it's just going to be wasting words. Keep the cast down and concentrate solely on the main character. It's simply to complex otherwise, because you'd have to have the three brothers each get something different out of their journey and for that they'd have to each be doing something of their own on said journey ... and you can see where this is going. You simply have too much in the story to make it work. Don't argue with me, I know what I'm doing. I kid you not, I've been writing for fifteen years.
I'd also suggest you look at using the in media res technique, which quite literally means "in the middle of things". If you start the story halfway through, you have less work because you don't have to write everything that happens on the journey. You choose which details are revealed to the audience and you choose when they are revealed. This will cut out most of the unneccessary exposition you'd otherwise be writing. Start the story when you main character finds the sword or when he encounters his enemy and you might just make it.
I share your sentiments on only writing stories that you feel are worth telling (though I'm not big on "only things that should be made into films", largely because films lend no time for more than simple character developmnt and I'm very big on developing characters), though I don't really think you're in a position to enforce it. I'm currently working the details of an idea I've had and the opening set-piece - a car accident and the events surrounding it - took almost three thousand words to write.
No-one is going to make you write something you don't want to wrie, but given your situation, I'm going to agree with what "everyone else" says: you really should be writing something simpler if only because you run the risk of failing terribly. Besides, do you even know anything about the samurai beyond what the average person has garnered from Hollywood?