He just negotiated an Agreement with Mexico re that problem using the promise of Tariffs if they did not begin to take some real action
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Sorry, that's not negotiation, it's bullying and one that will likely come back to bite the citizens of USA.
That isn't to say that there isn't an II problem on the US-Mexico border, there is, in the same way that some EU countries face an II problem from places such as Africa. I don't know what the solution is, I suspect you need to go to the country of origin of the II to understand why they think their preferred country of destination is the right place or a better place to be. In the EU, an immigrant is supposed to be "processed" by the country within the EU that they first set foot in, some of the EU member states, most notably France, seem to ignore that.
Until then, we have to be careful that we don't confuse legal immigration with illegal immigration with refugees