A common saying among admission counselors is that their job is to fill-out an orchestra, not simply finding the most talented individual musicians. If they already have their percussion section filled, they won’t pick another percussionist no matter how much better his/her stats are than the students who they need fill out their woodwinds, etc. Not to be taken literally of course. But the point is if they already had others who were STEM-focused with similar stats among the same gender and ethic group, they will seek those with lower stats that have a different background (like creative writing, theater, volunteerism, etc.). STEM-focus and high stats tend to go together in high school, so it’s not as unique combo. Whereas the theater student with the 1560 SAT, 5’s in STEM AP’s and hundreds of hours of community service is. And by URM I assume you don’t mean Asian as that’s that would be the opposite in this quadrant (thus the whole point of the current class action suit against Harvard and the previous rulings against the UC-system). With incredibly high stats like your child’s, yield protection (i.e. turning down those they expect to take offers from other prestigious schools) is also possible, though I’m not aware of Davidson having a specific reputation for that.
All that aside, anyone with such high stats still has a better than even shot at getting into Davidson. It just didn’t go that way for your first child. But if your other still likes the school, it’s worth definitely still worth trying. Good luck.