My friend’s D did a similar program at another school and it worked out really well. Since your D is excited about Hamilton and the semester in London it could work out very well.
Before making a decision I would focus on how Hamilton integrates students from this program into campus life for the spring semester – ex. will they room with friends from the program, will they be able to schedule their spring semester classes with the rest of the freshman, how do they get involved in ECs starting in the spring etc.