That looks to me to be a PO's attempt to stop a leak(s). I don't think Airstream ever used visible caulk inside the trailer like shown in your picture. (on edit: per Torii's post, looks like I may be wrong)
Regardless, Lee's advice of correcting the problem from the outside is sound. Your skin seams may need to be re-caulked (we used Vulkem & Sikaflex). Water leaks are tricky - even though the leak is appearing inside
the trailer at the windows, it may be a leak that is entering the skins somewhere else on the exterior.
The best thing to do to make sure the leak is found, is to remove all the old sealant from the seams on the exterior
with a popsicle stick (or something similar) and re-caulk all your seams & joints. There are companies that do pressure tests with bubbles to locate leaks, but on vintage trailers alot of the sealant can start to fail - so it may be harder to isolate a single failure.