I can understand the empathy, and I share it, but there has to be a firm reestablishing of order within the US immigration system, to include legal immigration. The United States should be treated like a Nation comprised of citizens again, not just an economic zone. Even if people view the US as one big Costco or Walmart, you can still be trespassed from those places.
I think something the Trump administration should explore is the option of beginning a grace period for illegal immigrants to return to their country of origin and apply for citizenship now. If they haven't by the time he enters office and they're caught, they lose the ability to legally do it in the future.
I also don't think we should be giving out as many work visas for certain sectors of our economy as we currently do, such as the tech sector, engineering (to include professors), mining, and energy production. There should be options for companies who can't fill roles with adequately educated Americans to tap into federal funding to train Americans for these positions. Exceptions could be made for immigrants coming from 5 eyes countries, but only if those individuals were citizens of said 5 eyes nation, and any money they send home should be taxed.
Programs like E-Verify should be mandatory, and companies employing non-citizens should be taxed at a higher rate, employers caught hiring illegal immigrants should face jail time.