Volleyball is a headcount sport so if @Loopy414 's daughter is recruited, she’d get a full scholarship to a D1 school like Pitt. Not recruited? Unlikely to get on the team at all.
If she wants to be recruited, that is going to make a big different. A D1 school is going to be all-or-nothing, whereas a d2 school can offer a partial scholarship.
I know she wants NO religious requirements, but she might want to consider Wheeling Jesuit as it as a large medical/training department. Jesuit schools do have a ‘religion’ requirement but there are many ways to meet the requirement like psychology classes, comparative religions, classes about certain authors like CS Lewis. I will also say that the farther south you get, any school can have a religious ‘flavor’ to it, and some of the sports teams even at public schools can be very religious with saying prayers on the field and having Fellowship of Christian Athletes a big part of the team.
Lindenwood University is now D1. It is slightly west of the Mississippi in St. Charles, MO and it is about 5000 students, but it is heavily sports focused (thus the change from D2 to D1) and has great facilities.