The trim you are talking about is a vinyl. In the wetter climates mold makes itself at home in a big way, turns it completely black. Where you are it is intense UV which first roughens the surface and then shortly followed by staining from blown dirt.
As you have found, virtually nothing makes it look new again. In fact, when you use bleach you further damage the vinyl. Anything you manage to get off comes back twice as fast.
Most of the time this trim is simply pressed into a slot and then held with self tapping screws every so often, and at seams and turns.
If you look in RV parts catalogues you will find that you can buy rolls of this stuff, but you have to know the thickness and width of your particular trim.
I'm sick of fooling with mine. The next trailer is going to have full body paint!