There are different problems I see.
What is your source for the tensile strength of the vine? As long as we don't know what material they are it is pretty difficult to assume any value here. So this is maybe the biggest uncertainty here.
What is your assumption for the 0.2 meters width of the contact area? An estimation from viewing the scene I guess?
But most important, we can't actually calculate AJ's weight with this scene because she doesn't use her entire mass to shut the window. She stands on her hind legs and only applies force with her forelegs. So we could only calculate this force she is able to apply this way. To calculate her mass she would have to stand completely on the vine (or rather stick to the window).
So the idea is nice, but it won't work.