Maybe you missed your calling to play Amos in Chicago.
POTUS always says ALL options have to remain on the table.
Re: Mexico's unwillingness to stem the invasion of "refugees" into the United States. I believe there has to be a "nuclear" option prepared. I would suggest that option be a military enforced SECURITY ZONE 50 miles INTO MEXICAN TERRITORY. Mexico has to believe that we are prepared to:
1) Forcibly enter Mexican territory.
2) Take control of all ports of entry to the US.
3) Destroy Mexican air defenses and air force.
4) Assume de facto control of Mexican air space.
5) Impose military security and law in the 50 mile security zone.
This would almost surely never need to happen. However, the Mexicans have to believe we would do it. We would get compliance in short order.
Obviously, that would universally be regarded as a crime against humanity. I'm talking about a defensible use of military to defend against invasion.