Both interpretations are technically possible, but when I read this firstly, I thought この only modifies 世界 (i.e., "this world"). That is, if I were to translate the Japanese title literally, I would choose "In a corner of this world." (Note that I don't know much about the movie. And I wouldn't say "In this corner of the world" is a bad translation, either. There may be a reason.)
片隅 is a word that vaguely refers to an inconspicuous place. Specifying it as "この/あの片隅" or counting 片隅 (like 2つの片隅) is not common. On the other hand, この世界 is a phrase I have heard hundreds of times. For the same reason, 世界のこの片隅に sounds a bit weird to me, although it is perfectly grammatical and possible as an eye-catching title of a movie title. Something like 世界のこの場所で sounds more "normal" to me.
In general, is there a way to specify which noun in a の series a demonstrative (この, その, あの...) refers to?
I doubt it. I think we are choosing "the most sane interpretation" almost unconsciously, case by case. When I hear この熊のぬいぐるみ, I would definitely interpret it as "this stuffed bear" but not "a stuffed bear modeled on this bear."