You could inform your daughter that she will have limited assistance from you and her father when it's time to foot the college bill, and show her the numbers. When she is about to leave for school, if you have done your job right, she will be in the middle of learning skills like long term planning, number crunching, and financial know-how.
This is what my parents did for me. Bless them, they spend like mustacians most of the time, but they've hoarded 100% cash on one teacher's income for their entire adult lives. As a result, they were willing/able to offer my brother and I each around $3000 per year in assistance while we were in school. When I was going to school, the EFC was about $20,000 / year.
Obviously you are much wealthier than my parents, but that doesn't mean you have to foot 100% of your daughter's bill for her experiences in college, regardless of where she chooses to apply and where she's accepted.
If you make it abundantly clear what she can expect from your contribution, no matter the circumstances, and that SHE is responsible for choosing the school (or no school), I think she will make a smart choice.
This is what my brother and I had to do. We were told to investigate the options on our own, and investigate we did, ferociously. My brother, the academic superstar, did it his way: high marks, lots of scholarships, and a school that specialized in his field with good financial aid, where he further advanced himself academically. He paid his ~$7000 / year expected student contribution through workstudy, summer minimum wage jobs, and minimum wage jobs for a year after graduation to pay off his ~$10,000 debt. He is now getting paid to attend grad school for his phd, and getting grants to travel and conduct research.
I, the introvert and school-fearing, did it my way; I made friends online, attaining a good social standing online among professionals in a lucrative industry while other kids my age were attending high school. I even got internships at a tech startup that would later flourish to a global success. Since I worked in tech already and I had a good reputation, I was able to get good paying jobs every summer during school. I chose not to work during the semester, I thought it was antithetical.
I was personally responsible for paying about $17,000 per year, much more than my brother, because I had no academic standing out of highschool, I was the last child to attend school, and the school I chose (Beloit College) jacked up their tuition a lot while my financial aid stayed the same. However, I only wound up with $20,000 of debt at the end, and I paid it off in one year after I spent 6 months searching for the right job and the right place to live. Now I have a good paying job and I am well on my way to FI by the time I'm 35, barring any "Thousand Year Flood" style depressions.
The knowledge that I would be responsible for paying that much (as well as my parents promise to charge me rent if I lived in their house after I was 18) instilled an empowering fear and sense of urgency in me that I learned to tame and channel through the years. I became exponentially better at making friends, I learned how to think like a business and get a good paying job, and best and most of all, I had to learn to be self sufficient and define my own standards of what was "adequate", "good", "too expensive", or even "disgusting". For me, that's what being mustacian is all about: choosing how you live knowing that you are responsible for the consequences no matter what happens.
I don't know your daughter, but I think that her choice is more important than your plans. What I mean is, that she is responsible for how her college years and her life turn out, not you, and not your money, so it might benefit her if you present the choice to her early on. As early as possible.