The first thing I would do if not addressing the rotten wood by replacing it would be to get some "Git Rot", an epoxy, and put it at least on the rotting roof. The Git Rot will at least stiffen up the rotting wood. I'd then treat the wall cavity with an antifungal. Then it can be covered. If you do nothing, all the wood will continue to rot and you just may lose the back end of your trailer.
Eternabond makes a variety of tapes, some that will conform to any curves or edging like Web Seal, which I've used. Web Seal needs to be painted after installation.
None of the Eternabond tapes will adhere to silicone sealant or any of it's varieties. I mean, any trace of it needs to be removed with a solvent. It sounds difficult but isn't. Buy some caulk remover (3M makes a good one), apply it on that mess of old caulk you have and cover overnight with Saran Wrap. Come back the next day and all of the caulk comes off with a rag. Use some acetone to remove any of the caulk film. Apply the tape and roll it with a small hand roller and your waterproofed for a good amount of years. Like said, Eternabond Roof Seal has it's own covering but Eternabond Web Seal needs to be coated.
I used acrylic roof coating to cover the Web Seal tape.
Tape applied around vent and over standing seam, also taped:

Tape applied over roof edge trim:

Finished roof with acrylic roof paint:

Good luck on the repairs.