I missed the part where you explained why Mexican citizens are entitled to emigrate here. See...they're not.
Sure. And a starving guy who can't find a job is not entitled to the contents of your wallet if he finds it on the street, but you'd have to be a sociopath or a retard to actually blame him for not returning it to you, even if that's a "right thing" to do. Or claiming that he's somehow a bad guy if he doesn't.
Shipping Mexican citizens into the US won't fix the problems in Mexico.
Those Mexican citizens aren't trying to solve the problems of Mexico as a whole. They're trying to solve the problems that they have as individuals.
And, of course, no-one asked them if they want to be citizens of Mexico when they were born, so Mexico is not entitled to having them solve its problems, either.
They don't have sovereignty, the Mexican state does. To what extent it actually represents the citizens in general, and these citizens in particular, is a question that you should ask before pursuing this line of argument any further.