Before you assume that Grinnell will be cheaper, see if the coach can get a financial aid pre-read for you. It also looks like any merit aid will be considered a “resource” when calculating financial aid:
“While scholarships are awarded on the basis of merit, they are considered a resource when determining eligibility for need-based financial aid. For example, if a student has $22,000 of calculated need and receives a merit scholarship for $25,000, this student would not receive need-based aid since the scholarship exceeds the need.” https://www.grinnell.edu/admission/financial-aid/affording-grinnell/scholarships
This sounds like to me that any need based aid would be reduced by this $10,000 scholarship, so I am not sure you can accurately call this an “additional” $10,000 unless you would be full pay otherwise. Best to get a definitive answer on this from the financial aid office at Grinnell if you are trying to sell Grinnell to your parents based on cost.