Notarization and Legalization are two different things.
Legalization is done with a foreign document to be used in Chile, as Chile is not a party to the Hague convention on signatures (not to be confused with convention on international child abduction). Thus, you can have a foreign notary signature legalized, but not all documents that are legalized are notary signatures (e.g. social security statements and birth certificates for residency). In the case of leaving the country however, just legalizing a foreign document may not be sufficient depending on what it is for. More on the process of notarization and legalization here:
http://www.spencerglobal.com/chile-lega ... ments.htmlIn the case of both of your deaths (not just say hospital or kids just departing the country with other grandma) things get a whole lot more complicated under Chilean law.
The short version is they will have to go to court to get guardianship certified, regardless of who it is. The good news is that in most cases the emergency hearing are fairly fast, as within a day or two in Chilean family court. Just be aware that things can be a whole lot more complicated, depending on any number of personal circumstances (e.g. foreign will, competing family members claiming custody). Thus, you want to talk to a Chilean attorney about your particular situation.
We recommend to all of our clients to have a Chilean will drafted, not only for dealing with their assets but also dealing with their children's custody if something should happen to them. You can not just scratch it on a napkin, and stick it in your hotel room safe.
More on Chilean wills here:
http://www.spencerglobal.com/chile-inhe ... chile.html