I am sorry that your daughter is caught in this kiddie trap tax. Like I said, that was not the intent of it. It was to stop parents from trying to shelter investment income in their kids’ name.
This is a pretty esoteric application of the tax code. It wouldn’t surprise me if a lot of graduate students and their families are not in compliance. However, I would call some schools up or talk to a specialist tax advisor before finalizing any plans. Maybe there is a legal way around it.
Of course, one legal way around the kiddie tax is for her to get married 
This might not be wise. It seems very hasty to tell your daughter not to try for fellowships. A lot of fellowships are only awarded in the last year of undergrad or the first year of grad. Fellowships are often better than TA or RA -ships. In addition to being more prestigious (which can be a plus in graduate school and on the job market), a fellowship can make it easier to get your first choice of Ph.D. advisors since having a fellowship makes a student “free” to the advisor. It also relieves students from having to spend time teaching and allows them to spend more time on their coursework / research. Even an extra $7,380 of tax for a year or two might be worth paying for this … it all depends.
If your daughter is lucky enough to win a fellowship like an NSF, these fellowships often allow you to “defer” them for a year or two (until she is past 24). She could defer it for a year and ask the department to give her a TA-ship instead for her 1st year.
I’m still not sure that this is necessary because you can arrange things so that she doesn’t live with you, but you know better than I. Of course, even if it’s not necessary I am sure your daughter wouldn’t mind getting some extra money from her loving parents
Anyway, although I am throwing out some angles to look into, there is a lot more research to be done.