Not many current students here, I would check Reddit.
You would need to contact people in DGS and ask these questions about admit rates, etc.
Engineering is tough, but I don’t know admit rates. Remember that engineering has its own separate undeclared students in Grainger, so those students are all looking to get into engineering majors, whereas only some portion of the DGS students are targeting Grainger.
If engineering is really what your kid wants, best to take a direct admit if they have that option.