It would work better as a class action lawsuit. Thousands of well-trained American construction workers are having the same problem you're having. Too bad the unions don't have any guts. They have the legal connections and financial where-with-all to get the job done.
Illegals aren't employed in construction just because they're willing to work for less. Contractors can get illegal construction workers to cut a lot of corners, to use substandard materials and/or do shoddy workmanship. A Korean contractor and his crew of illegals was working on the house across the street from us and we'd go over after they left at the end of their workdays. Shabby, shabby work. No insulation in the walls and the window frames weren't mitered. I don't think most illegals know how to miter a corner. The house was flipped and the young family that moved in really complained about how cold the remodeled section of the house was the first winter. I showed them the photos I'd taken during the construction.