It really stinks that most of the older or larger Catholic universities are misrepresenting themselves as being a Catholic institutions. Its pretty clear that the Catholic church has lost operational and spiritual control of this university and others. I imagine there are some very disappointed practicing Catholic students who have dreamed of going to a school like ND and they find the state its in.
How would they legally retake control of it? Hard to say. Revoke its charter? Do they really want to?
They would likely have to sack the entire workforce and restart the whole school at this point to regain control. Even requiring the employees to be practicing Catholics wouldn't do it, due to the amount of people inside the Catholic church (including priests!) that do not proscribe to Catholic teaching.
Oh, by the way, I am not Catholic.
Its no wonder people like Domino Pizza founder, Tom Monaghan has founded a new Catholic colleges like Ava Maria. So there are options out there. Seems impossible at this point in time to reform existing schools it seems. All the ivy league schools, which are about as secular as you can get today, were founded by various protestant churches as seminaries. Most still have seminaries (probably due to founding charters) but they sure aren't the focus of those schools and are the unwanted step sister for the most part. Some of the older pastors in my church denomination have degrees from Princeton, but few go there now (though the denomination is not the founding church of Princeton it was a school many went to). Used to be a prized degree round here, not so much anymore.
Seems they all drift left, and its hard to stop.
I imagine the small Christian college I went to will get more and more secular as time goes on too. Very likely due to not having a seminary at all, just a general theology department (granted a very good theology department) and being liberal arts.