ICE didn’t just separate the family units during incarceration, they also failed to reunify them on release. They also forcibly sterilized other asylum seekers which is a whole another human rights violation. The USA has also signed—though not ratified—the 1989 Declaration of the Rights of the Child which has more explicit protections. I believe this was confirmed in US courts as they quickly issued an injunction of this practice.
There is also the issue of why they are incarcerated in the first place. They have committed no crime, migration and seeking refuge is protected under international law.
The UN universal declaration of human rights is written to be easily accessible and understood by the general public. And given that it was written 75 years ago I think they did a good job. I actually recommend everyone to read it entirely in your native language, as it has probably been translated into it and will only take a few minutes. A beautiful document indeed.
The important thing here though is not how rigorously defined these rights are, but the spirit of the law is clearly saying that the family is a fundamental unit of society. Separating the family unit is a failure to uphold that principal.