This kind of separation happens quite a bit within immigrant communities, especially nationalities that have long waiting lists for green cards, let alone undocumented immigrants. Due to some quirks in the Visa system, you have to leave the country in order to change your status which runs the risk of delays or outright rejection. When the parents are on separate visas, one can get let through with the kids while the other is stuck indefinitely. Often times that means that the parent not granted a visa becomes an undocumented immigrant in the host nation and the other is forced to return home because all of their stuff and financial obligation/jobs are in the US. If they can't find a job in the host nation, the stuck parent often moves back to their support network in their birth country, further complicating things.