I mean, when Syrians want to be refugees in Turkey, they get tent city, international aid and surrounded by Turkish soldiers that will kill them if need be. It wasn't that long ago 'Ottoman' wasn't a piece of furniture.
But I think the turmoil in Central America, and Mexico, is easily cured. Just teach the refugees how to speak English, study HISTORY, economics, civics and get a fine education in revolutionary tactics, and send them back better prepared than the Bay of Pigs.
I understand not wanting to grant amnesty for breaking the law. Issue them a permanent, or temporary labor card. No citizenship. They already have a country they are afraid to go back to... no reason to allow them to stay here forever cringing every time the government picks on them, like it picks on us. Don't worry about them ever voting, there are enough dead voters and crooked election officials. That is how they play the game, they being the respective political parties, living in fear of losing their power. That was King George the Third's problem - he wasn't loved enough, respected by those far, far away and was sure there was Historical precedent for Kings losing the throne, or even their head.
Personally, if I had enough time left, I would seriously study Spanish to gain a command of the language. Then I would prepare to exploit the Latin American nations, one filibuster at a time. a person engaging in unauthorized warfare against a foreign country.