but assuming she's attending the school longer (or else why pay and do the hassle for just 3 months instead of MET or even enter on exempt and extend)... I think it's safe to assume she will be extending the visa every 90 days, at 1900b a pop.
my 9 and 11 year olds enter on visa exempt and overstay years at a time. They second check me at immigration leaving, reminding me that they are overstay and it would be better if they got proper visas, but that there's no penalty. I say ok. And we do it all over again the next time we go abroad to visit family. I can confirm that it's never caused a problem.
it would still be his child.... He's just trying to make sure he gets rights to stay in it's life... Regardless of the relationship. It's more like, do it as quickly as you can, just in case the relationship dynamic changes and it becomes more difficult to do later