I am confused. Is Reed full pay? Or substantial merit? What are the schools you can afford.
Unless you have excess retirement funds or are a very young parent, borrowing from retirement fund or borrow at all to pay even for Brown typically is not a good idea. Many, many kids have to take finances into account when choosing a college. If you can’t afford a college without raiding your retirement savings, you can’t afford it.
I will say it depends on how much you are talking about - borrowing a total of say $20K may not be a big deal. But borrowing most of the cost, may put your retirement at risk. Other thing would be to have daughter pay it back, but you never know what path she will take and if she will be able to afford to pay you back. Also, with the economy these days, you never know what will happen for this job.
You are not making her go where she doesn’t want to go, you are making her choose among the affordable colleges.