I'm in Chile right now and am travelling with a Poder as well.
The first time I tried to cross the border to Argentinia, the Aduana (Customs) told me, that the Poder is only valid if its made by someone with chilean residency, but that is not true.
Anyways in Chile you should always have the poder and the Apostille.
You can find a good step by step description at this link:
Overland Chile Travel - WikiOverland
The Apostille is registered online so the Aduana can check, if your documents are correct, but you have to make that very clear.
Once you have these documents, you just need some patiance at the border.
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