Cut the immigration quota of non-cooperating countries.
Exclude nationals of the non-cooperating countries from immigration amnesties.
Tax wire and other monetary transfers to the non-cooperating countries.
Federal law already requires the State Department to stop issuing visas to countries which refuse to take their criminal citizens back. It's being completely ignored along with most other law regarding immigration.
We could sue but the American people have no standing to challenge our lawless government. There are no redress of grievances available.