Have you and your daughter read this page?
http://www.ox.ac.uk/admissions/undergraduate_courses/colleges/how_do_i_choose_a_college/index.html
I am sure you know that the university departments at Oxford provide the courses, the colleges provide for the well-being/social development side of the individual. To that extent it doesn't mater which college is chosen.
Since your daughter is attempting to get onto one of the most difficult courses of the lot at Oxford (probably exceeded only by the demand for PPE), I would have though an open application was best.
The success rate (applications to acceptances) is about 20% - and she is going to have to have top A levels plus extras to stand a chance. Good luck.