While I am pleased to see our justice system work vigorously to rollback what it can, the administration showed a strong disregard for the law with these orders. It is unclear yet whether the Deparment of Homeland Security is even complying fully with the stays (the TSA administrator for Dulles refused to meet with a Democratic congressional delegation that went to the airport to make sure the judge's ruling was even being followed).
The Department of Homeland Security's own press release was scary in its own right claiming that they were deciding "at the moment" to comply with the court's ruling.
It's important to remember how much our system relies on tradition to operate effectively. The law/government is not a perfectly reactive state machine. It assumes a certain level of good faith and judement from all the nodes, and the executive is a powerful node in the graph, it has the ability to clog up its edges and render a lot of the other nodes feckless.
I think a lot of what Trump has done has been horrifying, but I, like you have felt that it has been in line with what he campaigned on and legal. In this case I simply have to disagree. This is over the line.
I know, I think everyone knows this. I didn't vote for him because I was afraid he would follow through on his promises, not the opposite. I don't get why people keep bringing this up as an argument in favor of the order. The fact that you promised to do something does not mean it's a good thing to do.
https://lawfareblog.com/malevolence-tempered-incompetence-tr...
More likely than not, they just wanted everyone to have a SSN so they required it for kids. But non-residents cannot have SSNs (even if legally there), so they had to make an exemption for them.
In a way, you can argue the opposite. By making sure that kids have SSNs, they get access to credit and much more, while those without SSNs get stuck in a limbo.
In fact, you would be surprised at the number of doors that close if you don't have ID or have that crappy ITIN. EG: while I was studying, my friend only had an ITIN on his first year, and it sucked really bad for him. No access to credit, no access to most rentals (because no credit check to run!), etc. Even stuff was more expensive, as I could get the 10% Target discount and he couldn't.
(I was lucky enough to had a SSN from when I worked with a sort-of-diplomatic G4 visa, and it was incredibly useful, and allowed me to get a good credit score, a nice apt close to campus, etc.)
I understand that you are annoyed by having to hand over information about your kids to the govt, and maybe the process of getting them a SSN is a chore. But believe me, both legal and illegal immigrants would love to have SSNs.