Finding causes of problems as well as solutions in economics is actually very simple. I say solution but problems are not actually solved. There are trade offs instead. Society gains the most when trade offs result in the most positive outcome. That is all that can be done.
Almost any economic problem is caused by a lack of faith in the free market system. Solutions are seldom seen because the solution is distasteful or at least requires deferred gratification. Countless hours and dollars are devoted to coming up with palatable solutions none of which are viable. A constitutional amendment promising the separation of government and the economy would benefit every living soul in the country. Such an amendment is not possible because free markets are not trusted.
The immigration issue is nothing more than a labor market issue. People in the United states are paid a lot higher to do the same work that people with as much or more education receive for doing the same work in other countries. Laws passed in the United States for the purpose of rigging markets have a devastating effect on third world nations. When the gasoline industry was rigged so that all gas contained ethanol third world people could no longer afford to eat. U.S, drug laws which do nothing to prevent usage, provide high profit margins for the drug cartels in Mexico. Crime has taken over Mexico and had destroyed many natural opportunities. All of these things encourage immigration.
There is no way to slow down immigration with out doing one or more of a few things. The only way to stem the tide without reforming U,S. Drug laws and economic policies is to be completely brutal in enforcing the law. This is the way the Berlin Wall functioned and it worked for the most part.
The only genuine non violent method that will work is to return to free markets here in the U.S. and repeal laws that impoverish citizens of poor countries. When there is such a huge gap in what comparable jobs pay in different countries, countries that pay well are going to get immigrants.
This solution is not viable right now because its implementation would require faith in free markets and that is lacking world wide. I promise, no other approach would generate as positive an outcome.