From what I've gathered over the past few years while attending a community college, it's up to the particular school to decide whether it's against school policy to carry something in your pocket.
Being in a more relaxed community, I can get away with having my AR-15 in my car, pepper spray in my pocket, as well as a large hunting knife attached to my side. Try that out in Blacksburg and you'll end up in handcuffs.
Basically, call your daughter's school or look through the handbook. I would imagine that mace (especially since we are dealing with a female) would be legit.