Can you post a close up picture of the leaves ? :) Arum

Is your planet sideways to ours? your trees look funny. :)

So far you haven't really shown us the vine you want identified. The pictures show two different trees and no detailed views of the stems or leaves of the vine. It is not very usual for a vine to actually kill a healthy tree, unless you are dealing with tropical strangler figs or something. And even then it takes years. So there might be another reason why your trees are ailing.