Honest Junior has a good answer. However, the general rule that is almost universal all around the world in every tax code - "Residents are taxed on world-wide income, non-residents are taxed on local income only". You can look up Deloitte, KPMG or EY tax highlights. They cover pretty much every country every year - i.e. Google "Argentina highlights 2018" and on a first page of results, you get a nice PDF document from Deloitte that gives you a summary. This does not constitute final conclusions but gives you a good starting point for analysis. Once you have read the highlights, you can ask the right questions from a paid consultant. If you go completely unprepared, your bill will be much higher.
Citizenship does not matter, unless you're a citizen of USA or Eritrea.
Here are the general defaults
1. If you have kids younger than 18 and/or wife in country X, you're in 95% of cases considered tax resident of X even if you spend no time in that country yourself. Young kids and/or wife is considered the strongest indicator of residence among all. Both over-rule all identity cards and passports of any nation. If there is no double tax treaty in place, the country where your wife and kids live has the 1st right to tax you. Countries Y and Z who also consider you their tax resident can only tax you on the remainder - if country X taxed you for 25% but county Y has tax rate of 30%, they may tax you for the remaining 5% but not more. Such situations are typically resolved in double tax treaties.
2. Of secondary importance, after place of residence of your young kids and wife come the days you spend in a country. Typically, if you spend 183 days in a country, you're resident. If you spend less, you're just a tourist with no tax obligations, unless you earn income in that country during your stay.
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There are more indicators but I stop here to avoid content bloat. Just read the highlights of Deloitte, KPGM and EY. Then formulate your questions. Once you have the (as specific as possible) questions, have a paid tax consultant who is familiar with the local laws look into your case. So in your case, someone who knows about Argentina and Chile.
Regards,