Here are the products I use. The list below is not complete; others prefer different caulking materials, but those below are among the most popular:
Proflex Bright White
Dicor Self-Leveling Caulk
Dicor Non-self Leveling Caulk
I use Proflex on vertical and horizontal surfaces where a bead of caulk is needed (but Proflex should not touch roof membranes). I also use Dicor Non-self leveling caulk on vertical and horizontal surfaces where a bead of caulk is needed if the caulk touches the roof membrane, but prefer Proflex if the caulk will not touch the roof membrane. I use Dicor Self Leveling caulk on the roof around seams where a wide band of caulk is needed; it sort of oozes out and makes an even surface.
On the side of the trailer where you see cracks in old caulking, remove any caulking that is loose or looks bad to you. Otherwise, clean up the dirt on the caulk with a solvent such as mineral spirits sparingly applied to a rag. When clean, put a new layer of caulking (I would use Proflex) over the old and smooth it if needed with a finger dampened slightly with soapy water.
The roof and all its seams should be checked periodically looking carefully for cracked caulking. Pull off any old caulk that is loose; otherwise leave it in place. Clean the old caulk with a rag moistened with mineral spirits, being VERY careful not to get the mineral spirits on the roof membrane. Then re-caulk with whichever caulking is appropriate.
There's lots of advice and information in forums... sometimes it is correct. For example, all of my posts are made by a political appointee who got the job as a reward for contributions to my diesel bill.
2011 Jayco 28.5RLS; 2008 Chevy Duramax; Pullrite Superglide Hitch