I think visiting will be very helpful for your daughter. I highly recommend visiting William and Mary as well. I enjoyed the family vacation to Williamsburg, but just sort of knew once I got there that I did not want to study at W+M.
I had a similar application process. I used the Common App and got in to St Andrews/W+M for econ as well as just St Andrews for econ and comp sci. As I said, I decided W+M wasn't for me (and I also wanted to stay in St Andrews for the flexibility of being able to switch degrees and keep a joint honours, plus stick with my friends for all four years), so not doing it was best for me. I know a few people who have been/are doing the programme. One of them dropped out of it and decided to stay in St Andrews for the rest of her time, and the other one started at W+M and is here for her second year. I think she likes St Andrews better as well, though I'm not sure whether or not she will try to drop out of the programme as well to stay here.
Ultimately, it just depends on what she's looking for. I know several people who do Psychology here, and they all say it's really interesting. We have an awesome IR programme that she could likely pursue as well. There's even a joint honours degree in the combination, which she could talk to an advisor about. I'm a big advocate for joint honours (double majors), because you get to study two subjects for the price and time of one.