No idea whether gpop's idea would work or not. But if you do pursue that avenue, I'd strongly suggest you keep the bit about planning to leave the country to yourself until you actually have sole custody.
I am pretty sure that even if the idea is workable in principle, planning to leave the country with the child would surely work against you if not destroy the endeavor outright. I'm sure a lot of judges would not take kindly to the idea, both on general principle and out of an assumption that leaving Argentina can't possibly be the best interest of the child (ridiculous as that may be).