Any non-citizen who enters the United States should be DNA tested.
Testing any non-citizen entering the US is way too intrusive. But anyone apprehended for entering the country illegally should be fingerprinted, facial and retina recognition obtained, and dna tested so the Government has all the information that could be used for confirming identity and if they commit further criminal acts it can be recognized who they are.
Confirming parents to children would be a great benefit and traffickers could then really be prosecuted.