While the movie has latin american themes, it doesn’t ever specify a country. From the first movie, the parents met after they were both sent to kill the other one. Eventually both parents are working at the OSS. Did one parent defect? Was this inter-agency drama?
If one parent did defect, which parent changed sides? This part of the movie was set late in the cold war, which opens up a lot of different ways this could go (unless it was stated explicitly somewhere).
Spy Kids lore is not something you can simply dip your foot in. Even Christopher Tolkien balks at deep diving it.
Maybe one was a double-agent, or under cover, and a miscommunication within OSS resulted in one trying to kill the other?
The idea of one of them having worked for an independent third party, that isn’t tied to the government also isn’t out of the realm of questioning. Floop almost certainly isn’t the only person out there with OSS-level tech, and the ability to put together a whole organisation.
A third party would make a lot of sense, then one or both started working for the official organization.
Which brings another question, is the OSS even tied to a particular country, or are they also a secret independent “third party”
The OSS, seems fairly solidly American. They have a direct line to the American president at points. In our world, the OSS shut down, and was replaced by the CIA/NSA, but that isn’t the case in Spy kids.
