As Heathrow Harry said, Argentina's best option is to develop a strategy that will make it more attractive in the long-term for the Falklanders to adopt allegiance to Argentina. There was a recent example (much feted in Argentina) of a Falklander who adopted Argentine citizenship, because he thought it the best long term option for his children. If Argentina were to concentrate on consolidating its sporadic progress to becoming a stable, prosperous and respected democracy then perhaps more FIs would take the same view. It would be considerably cheaper for Argentina to spend on incentives for FIs to become Argentine (eg fund local schooling, health care to compete with UK provision, and offer free tertiary education and healthcare on the mainland) than spending on a military solution.
Bear in mind, also, that the bellicose and populist statements of Kirchner are not universally applauded in Argentina. I'm from an Anglo-Argentine family, and even have second-cousins serving in the Argentine military - they and most of their acquaintances are appalled at Kirchner's populist pronouncements blatantly aimed at voters who are the Argentine equivalent of "The Sun" readers in the UK. Unfortunately there are a higher proportion of them over there than in UK.