I'm with hosspuller on this one.  Take a very sharp linoleum / utility knife to start with and remove ALL the old caulk. I've never had to use any power tools, but I bet a Dremel with a sanding disk would work good in that kind of area.

There are several de-gunking products that are safe to use on powder-coat or painted surfaces... check with your trailer dealer, RV place, or car/truck automotive dealerships. Use this to remove any little bits of caulk.

Wash the area thoroughly with soap and water and rinse well (vinegar in the rinse water won't hurt.) 

Once it's really clean, apply caulk of choice. I always use white, as that's what color my trailer is. : ) 

Take a very sharp linoleum / utility knife to start with and remove ALL the old caulk.

This may work on a steel trailer, but don't use any sharp tools on an aluminum roof or aluminum product. If the metal is scored by a blade, it will set up a positive area for localised corrosion. Very quickly you will have a weak area and in time can have the metal actually split and fail along the line.

For proper caulking on any trailer, the old material should be first removed before any new caulking is added. Rigid plastic putty knifes work well, grinding the corners of your old broken screw drivers can produce a tool that will dig out caulking in seams. Cotter key extractors can dig into corners.

Brass, nylon and teflon wheels on a drill can clean off the metal's surface. Scotch Brite in many grades from fine to coarse paint removal can be found at the big box stores. They will clean and polish the metal without damaging its surface. If you have a sander with a hook and loop pad, they will stay in place without being physically attached to the sander.

Be careful and don't inadvertently cut or score the aluminum metal.

Just completed my trailer seams. I found that after removing all the caulk that I could with a 7 in 1 putty knife, a brass end brush chucked in a variable speed drill turning at very low rpm removed the remainder. A fast rpm would just smear. A nylon brush just smeared the caulking. I assumed because of friction heat. Acetone was used to clean before caulking with sikaflex 221 gray. Working in the shade out of the sun seamed to help. A very thick layer of caulk works best. I also found that bluemagic metal polishing cream did a very good job of polishing the rest of the alumnium trailer. I purchased Bluemagic at a truck stop. I might add that I experimented with many ways before I settled on these two tips. Hope this helps.

What did you chulk with?  was this a steel or Alum trailer?  and what was the name of the tape?

I had someone tell me to use Tar Tape but when I went to the hardware store they didn't know what I was talking about.  I have a steel trailer I want to reseal.  Thanks