There is a doctrinal obligation to control the border for the common good. There is a doctrinal obligation to welcome the immigrant where it is reasonable to do so. These obligations are, in current circumstances, contrary to one another, and it involves a prudential judgment to decide which takes precedence. As you said, there is no doctrinal obligation to bar entry, but equally there is doctrinal obligation to permit it either.
As for your analogy, discrimination is contrary to Catholic doctrine, which is why your analogy fails. With immigration both of the competing options are supported by doctrine. And no, buying a house in whatever neighborhood you want is not a fundamental personal right. It is a legal right. Finally, your analogy fails because what is at issue with immigration are doctrines pertaining to the obligations of government; in your case there is no government involvement at all. Just because you can envision cases of competing interests doesn’t mean you have identified something analogous to the immigration issue. With immigration the government has competing obligations. It can meet one obligation only at the expense of the other.
And while the bishops have not said we must free the adults, they have said the children cannot be separated…which leads inevitably to that end. It’s like saying “When you come to the fork in the road you cannot go right” and claiming you have not said “You must go left.”