Leaked calls between Mexico and Trump say that Trump has told the Mexican Government that he'll send troops to the border—including across the border—to deal with the violence that the Mexican government is unable and unwilling to deal with.
This has been denied by both the White House and the Mexican Government.
However, the basic principle that the United States has no moral or legal obligation to respect the sovereignty of Mexico, which has never respected the sovereignty of the United States, can certainly be applied on a smaller scale to places like the Coronado islands, an unoccupied island claimed by Mexico which is used by smugglers to bring illegals and drugs into the US. [Deserted Island Being Used By Illegal Immigrants: Immigrants Make Stop At ‘Smuggle Island’ On Way To United States, 10News, November 8-10, 2010.]
You see this boat? It's a "panga boat" used in smuggling, and the only way a boat of that size and shape can make it over the open sea from Baja to the California coast is to stop at an island the US Coast Guard isn't allowed to land on.
So, as I say, we've twice suggested doing something about it. The previous two administrations weren't interested, but Trump might be.