Let's assume FallenAngel is right and the judge does not like my situation and citizenship is not granted: What happens then? Can I get back to scare one and apply for permanent residency?
You have a solid case. You are married to an Argentine and most importantly have Argentine kids. You do not need to meet any time period or residence. Your case is vanilla, as long as you do the paper work and wait (18-24 months-ish). I don't think you even need a lawyer.