I do not see a problem with the directions. Better to go to the processing center and get sent back rather than disappearing and never be found to be sent back. I know about Gohmert since he is in Texas and been in government for many years. He is prone to believe far out conspiracies.
So direct them back across the border, where they came from.
As for the third Obama term, doing the outrageous (like making sure bulk sales of weapons were made to cartel buyers, only to have those weapons show up at crime scenes later, to use to push for gun control here) is a hallmark, a feature, and not a bug.
The more outrageous the crime sounds, the easier it is to pass off as just "conspiracy theory", and they use that.