You have the answer! The problem is the the US/Mexican border is too wide. However the southern border of Mexico is quite narrow.
(enable sarcasm filter)
I propose this solution. We make Mexico the 51st state and grant them all citizenship. We dissolve all forms of government in Mexico and replace them with a red state form of government. We kill all the drug cartel members with snipers or an open hunting season.
They will no longer have any reason to come north. Problem solved.
(disable sarcasm filter)
I used to think America should have expanded all the way South to the Panama canal. For that very reason.
But the welfare state destroyed that idea.
Now we are screwed no matter what we do, it not a matter of if we will collapse only a matter of when.
despite your sarcasm your solution would work better then theirs.