Lots of good questions. Let me start with some thoughts, and many other members will follow up.
How many watts in the panels? Stay away from the little panels, like 15 watts or 25 watts. General concensus seems to be that two or three 80 watt panels is pretty good. You would have trouble carrying more than that, though it could be done.
Your panels could either be roof-mounted as you describe, or portable ground-mounted. Roof-mounted are easy to use, but depend on parking your TM in a spot that will be sunny all day. Although you get lots of electrical power, your trailer becomes uncomfortably hot inside, especially if you are camping in the desert. Ground-mounted enable you to park your TM in the shade, moving your panels into the sun and pointing them south no matter which way the TM happens to be facing. Lots of discussion in the Solar Power forum.
You need a controller, whose function is to stop the solar system from over-charging your batteries when they are full. A simple and cheap controller is perfectly adequate for the small systems we are discussing. More expensive controllers (called MPPT) will extract more charge from each hour of sunlight, but for a small system are so expensive that it is cheaper just to buy another solar panel if you need more capacity.
You can run the solar charger system and any other charger at the same time. No need to think about switching one off and another one on, etc.
Try going to Arizona Wind and Sun
http://windsun.com/ for a lot of good info. Although they sell solar setups from an associated web site, their mission here is to educate potential solar users so they know what to buy.
Hope this helps.
Bill