Hi Teresa,
So what does your daughter like about product design? What kind of projects would she like to work on?
Industrial Engineering is completely different than Industrial Design. I would not like to think of Engineering as a foundation for another career. Also, would she be willing to spend another 2-4 years after Engineering to study product design?
Having a full ride for Engineering makes it a tough choice. I would recommend visiting or talking to counselors at 3 of the design schools you mentioned to learn more about it and really understand their programs and focus. You didn’t mention Art Center in Pasadena which is another top school.
Stanford has a great Engineering program + a product design program. The design program might be more theoretical but it might be a good compromise.
Good luck.