You do know that composite is limited to SD (NTSC or PAL) resolutions? The quality of a composite analogue signal compared to a digital HDMI signal is miles apart. There's no real point in playing BluRays if you're outputting to composite, you might as well stick to playing DVDs. You'd certainly have to go through some kind of down-conversion to go from HDMI to composite - unlike DVI, HDMI is purely digital, so there'd need to be some kind of box in between, although I don't see the point of taking an HD signal and converting it to an SD signal. Frankly, you'd be better off using the VGA port if the motherboard has one, and use a VGA-Composite dongle if you can find one.
I don't think there is a way to force TMT3 to output to a particular display (its options are really quite basic), I guess it depends on which display it starts on - Windows should remember this setting if you drag TMT3 to a particular display and close it from there.
You might want to take a look at PowerDVD9 to see if that's any better at using a particular display (I seem to remember that its options are more in-depth than TMT3's).