Unfortunately, the Constitution vests all executive power in the president of the United States. This means that all power to enforce the laws, to decide how to utilize the resources at the Executive branch's disposal, and to prioritize which laws are enforced using the limited amount of resources at your disposal, are solely the prerogatives of the president of the United States. The other two branches can't really tell him how to do his job, because his branch is independent of the the other two. As long as the president, breaks no laws, I don't think there is much we can do about it. You can sue for damages in court for consequences resulting from how the president enforces or does not enforce the law, but the courts power over the Executive Branch is very weak. Even if the court, did tell the president to enforce the law, he could refuse to do it.
The only remedy that there really is against a president who refuses to enforce a law passed by Congress is a political remedy not a judicial remedy--impeachment. If the president willfully refuses to uphold the laws passed by Congress without good cause, he should be impeached for willful subversion of a duly enacted law, for violation of the oath of office, for usurping Congressional power, or for whatever other crimes and misdemeanors with which Congress should seek to charge him.
Unfortunately, this is also a weak remedy because Congress never seeks to use its power of impeachment against offenders; or if it does levy charges of impeachment, conviction on the charges is virtually impossible even for obviously guilty parties, because no party votes to convict its own.
How does this square with the Impoundment Control Act of 1974? That came about when Congress passed funding for certain programs, and Nixon refused to spend the money on those programs. If Congress budgets money for immigration enforcement, and the Executive refuses to enforce immigration, wouldn't that be a case of impoundment?