I have no personal experience with this, but I think the question can be analyzed without that based on the assumption that your primary concern is moving with your family to the Netherlands. I conclude that you should decide where to file the application based on the date of your move.
You say that it will take up to one year to get all of the documents in Argentina. Moving to the Netherlands will be easier if everyone has Italian passports, so you should apply for those in Argentina if you will be moving to the Netherlands in May 2018 or later.
Moving to the Netherlands will not be significantly harder, however, if your wife and daughter are traveling on their Chilean and Argentine passports, because they enjoy freedom of movement under EU law when they are traveling with you or traveling to join you. This is controlled by Directive 2004/38/EC.
So, if you don't want to worry about whether there is enough time for them to get Italian documents before you move, just move. Citizens of both Argentina and Chile enjoy visa-free travel in the Schengen area, so they don't need to apply for a visa. They only need the following documents:
- your Italian passport (to prove that you are an EU citizen)
- your wife's Chilean passport
- your marriage certificate (to prove your relationship)
- your daughter's Argentine passport
- your daughter's birth certificate (to prove your relationship)
- Evidence that you are already in the Netherlands if they are traveling without you
The marriage and birth certificates should have an apostille. The agency that issues these documents should be able to refer you to the procedure for getting this.
Once you are in the Netherlands, your non-EU family members must apply for a residence card within 90 days. However, if they're actually Italian citizens, they don't need a card; they just need Italian documents. You should therefore go to the Italian consulate there and apply for them.
The path for your wife to acquire Italian nationality depends on the date of your marriage. She may already be an Italian citizen, or she may need to apply for naturalization. If she needs to be naturalized, then she should apply for the residence card in the Netherlands while awaiting naturalization. Once she is naturalized, she no longer needs the residence card.