I've seen a lot of people far more well-informed about US politics and law say that there is no such law - this is a pure policy decision by Trump.

Can you cite the law he's required to enforce here?

Sure: https://cdn.ca9.uscourts.gov/datastore/opinions/2016/07/06/1...

That does seem pretty unambiguous to me: if they're holding the parents for immigration offences, by law they have to separate their kids from them because they cannot imprison the kids too. I think the US media is outright making people less accurately informed on this. The most I've seen is a brief mention that "US protocol prohibits detaining children with their parents because the children are not charged with a crime, while the parents are", without explaining what this means and the fact that this is a legal settlement that the US administration cannot modify.

To give you some idea of how badly you and everyone else has been had by the media: in the hours since you posted this comment, the New York Times found out that Trump was planning to stop separating families at the border and simultaneously decided that actually, this legal restriction - which the entire press had convinced everyone Trump just made up - exists after all and will probably stop him from doing so. https://www.nytimes.com/2018/06/20/us/politics/trump-immigra...

Not only is everyone going along with the new narrative, they're confident that Trump supporters are the ones who are too blind to see that today's talking point contradicts the previous talking point.

Trump is not required to enforce it. He could exercise the same discretion that Obama exercised, but he instead chose to implement a zero tolerance policy.