Ed be sure to ignore advice that is offered if'n you already have a fair head on what you want to do... but - having said that.
As some have indicated PT is overkill and has drawbacks, I'd say about now that I think a 2x10 is too much. But you have the visual, so do what you will. On my little camper (not much smaller than yours) a past owner had "shor'n up" with a pair of 2x6s to fix a weak build in the back (kind of sub boxes behind the wheel wells) and man what a hoot I had pulling them out to rethink the whole setup they placed. That's right about here in my build - you might get a hint or two.
Structure and New Wood page two (by my count)That particular thread (before and after I think) will direct you to pics of my camper corners, framed in 1x2 and covered inside with 1/8" paneling, outside with aluminum. Not much there. Front and back walls had 1/2" plywood, but you are on the right track with your inside corner idea.
I'll also see if I posted a hint at how my future plans are for my tie downs. Your main idea here is to strengthen the downward pull on your tie-down spot. Any upward force is the other thing (jacking). Maybe the jacking is why you're thinking 2x10? All you need is something to spread the load over what is probably a 1/2" plywood wing (the horizontal member where the jacks fasten). So maybe more 1/2"? That would be a total of 1" plywood. Probably plenty.