i would suggest looking at some AMD Zacate boards-- the processing, and graphics power and overall power consumption is supposed to blow atoms away.
for a board like that, it uses a 19v power supply, so you simply need a power supply that outputs 19v--either carnetix unit, or dcdc-usb, or a couple other units in the mp3car store should meet those needs.
you said that you will be using them for second screen duties, so the primary concern-- not being able to enter/see bios is not a issue..
and yes, they do bypass the onboard graphics, but worse-- they use the system processor for any data that they receive.
i have a 7" proximus usb screen-- in my tests, expect to require at least a board with a pentium dual core, or better processor-- on my laptop, the usb screen would send the cpu to hover around 50-60% usage while playing a youtube video. overall, cpu usage was around 15-70% depending on screen usage..
though i haven't specifically tried it on my older atom board, the results on my pentium-powered laptop are enough to worry me that it won't run good..
i don't have a huge amount of experience with playing different video formats in-car, but overall, onboard graphics-- even intel integrated chipsets still seem to handle HD movies decently.
but if this is a concern, i recommend getting a board with multiple video outputs, and with a better-then-average video chipset. i personally run a zotac board with integrated geforce 9300 graphics-- so far, i haven't had many problems with it.. though, i never bought it specifically because of the graphics, i bought it because it used a socket 775 processor..