i don't really understand the need for 1080 resolution.. most of the time, it is unusable in-car.. i really don't believe you will be able to tell a difference between a 1080 resolution image, or lower res. with anything smaller then at least a 20" screen.
you will also need to take into account the way that any FE you use will display. at that resolution setting, it might not be fully supported, and could result in a interface that is dangerous to use in-car.
infrared is a horrible solution for in-car use-- the sunlight will mess with it, and at certain times, will render the display useless..(the suns warming rays are partly composed of infrared, so many times the display will have trouble understanding if it is seeing it's own infrared signal, or the suns signal)
at this time, the only options i know of in-car for touch is capacitive, or resistive.(though lilliput is about to release a SAW screen[7"], and there are also projected-capacitive-touch screens, though i haven't seen those in-car)
at this time, this might be your best option..(are you ready to pay almost a $1000 for a screen?)
another thing to keep in mind is that you could look into building your own screen/controller combo-- there is a link somewhere in this lcd section about using laptop screens, and a company that offers controllers for them. you might be able to use that as a solution