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As a clarification, our understanding is Princeton Engineering allows more room for non-engineering electives than Olin. The compromise would be taking less engineering courses at Princeton than at Olin.
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The engineering courses that are required are dictated by the ABET accreditation, so you may find minor, not significant, differences from school to school. My D was accepted at Olin and she was concerned about the number of humanities courses she could take as she wants to be a well-rounded engineer. After discussing this with Olin staff we were assured that her desires could be accommodated, although it might require more effort on her part. They were very willing to work with her to construct an individualized program.
She was also accepted at Columbia where she found the Columbia core attractive.
After being accepted at Duke we asked about their flexibility and it was very much dependent on the department (Mech E was very rigid while Civ and Env E was willing to accommodate).
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If your daughter plans to work as an engineer, she should major in engineering and take as many math classes as she wants to.
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Whether additional math courses will be beneficial depends on what your D wants to do once she completes her first degree. Soon the MS degree will be considered the first professional degree in engineering and graduate study in engineering will provide the opportunity for further studies in math.