As an FYI, students at Loyola New Orleans and Tulane are able to take classes at the other university and to eat in the others’ facilities too, I believe.
With your daughter’s interests and focusing in on Catholic schools, has she considered:
Catholic U (D.C.): It’s about 3k undergrads, but D.C. is a hard place to beat for your D’s interests. This would be a likely admit.
Seton Hall: About 6k undergrads just outside of New York City, and if your D’s interests lean towards international politics at all, they have a very interesting diplomacy program. They also offer a semester in D.C. that many of their political science majors can take advantage of. This would be another likely.