I would support everything Yo says above. However, with regards to your message about your daughter I would add my story.
I went to Virginia Tech, and similarly to your daughter was on more of an engineering track with really high math and science scores (more so than art and sketching skills). I did not plan on studying Industrial Design, mostly due to lack of awareness for the program. I was very fortunate to attend a school that had a lot of well respected programs so switching from architecture/engineering to design was not a detriment (or a challenge like it would be for a lot of schools). I bring this point up because if she wants to dabble in both engineering and design to find a solid mix of both some schools are better than others at doing so.
Also, product design seems to be trending towards having designers and engineers more overlapped in skill sets. An Industrial Designer that can sketch and knows mechanical properties is much better than one who can merely sketch concepts and VV an engineer that can communicate visually is more beneficial than one who has an untrained eye for aesthetics.
Hope it helps!
-Pb