"Why are any of these illegal criminals in this country? I am furious that the Federal Government allowed this criminal to stay in this country and KILL my son!" the mother wrote.
Mendoza also called for tighter laws that would prohibit immigrants illegally present in the United States from purchasing and registering vehicles without a driver's license and would remove immigrants who are illegally in the United States and convicted of a crime.
The White House did not respond immediately Thursday to a request for comment.
Court records show that Corona had pleaded guilty to a criminal-conspiracy charge in Adams County, Colorado, and prosecutors dismissed charges of burglary, assault and leaving an accident scene.
Corona was a native of Chihuahua, Mexico, who had entered the United States without permission.
Corona, 42, collided with Mendoza after driving 35 miles in the wrong direction on three Phoenix-area freeways as other law enforcement officers responded to calls about the wrong-way driver and scrambled to intercept him.
Mendoza, a 13-year police veteran, was on his way home from work when he was killed.
Corona's blood-alcohol content was 0.238 percent, the Arizona Department of Public Safety said. A driver is presumed to be intoxicated in Arizona at 0.08 percent.
Mendoza said in the letter to Obama that her son was half-Hispanic and that she has no issue with immigrants who don't commit crimes.
"But when you go into another country ... and commit a crime, that's where I draw the line," she said.