I've been involved in this with cine 16mm - but not using beam splitters ...
Prob best to start a new thread on it as to keep this one one topic (post pics of your camera here, once you've built it)
But yeh, you'll need a 2/3rd 1/3rd split mirror for the first split then a 50/50 for the second (1/3 goes to the first film, then %50 of 2/3's i.e. 1/3 to the other two) - then you'll need your three wratten gels or filters with quite a hefty intensity reduction in each to split the colors adequately, Hope you're not planning on photographic moving objects ? exposure might be too long - if not then consider using no splitters, and changing filters for three consequtive shots instead (what was done in 16mm). Have a look into Kinemacolor also.
As for precision & rigidity- where to begin !
um, just - er, - hrmmm - build it well ??
ok, think about this: while you are building the camera think about the process of verifying its output in terms of the output specifications you're after, once you're happy - you're happy - happy is happy = done...
If not, then look at what you're not happy with a deduce what is causing it, then fix it.
Every camera has faults - it's how picky you are that defines them
Long winded way of saying that maybe we can help with specifics once you hit a specific problem, but for now, it really is too hard to give advice. Hopefully someone will prove me wrong ?
btw, googling 'one-shot camera' and having a quick glance doesn't give any related hits
edit: just had a look at Edmund optics - interesting they dont do a 66T/33R or 33T/66R splitter huh ? And yes, go with the AR coated ones if you can - mind you, the natural responce of the filters involved will probably solve any bounce back issues - something to ponder