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I would recommend that you go along the entire perimeter of the inside of your trailer and see how many other rotten spots you have. If you are lucky, the ones you have already identified will be the only ones, but you may be in for a surprise. IF it is a big surprise, you may be ahead going for a full floor replacement (ie., shell-off) rather than patching here and there.
At any rate, assuming you are going to go the patching route, then yes, it is nice if you can get the edges of your patches to fall on a support. If you can't don't fret, just add an additional piece of wood to splice your patch to the surrounding floor from underneath (screws will go in from above so you don't need to drop the belly to do it).
I don't think marine grade plywood is necessary, especially in a patch. I doubt seriously that the original floor was made of marine grade. Besides, the marine grade is higher quality (more layers, less voids), but will rot if exposed to water. Figure out where the water is coming from and make sure it gets stopped, and finish your patch job by soaking with polyurathane, and you should be in good shape.