Hi Gempony,
The school will always consider the best one among all your available score. In case you take your GMAT again and score higher, the Business school will consider the higher score. Alternately, if you get a lower score in your second attempt, the Business school will consider the higher score that was higher. All in all, Business school will always consider the highest score among all your scores, irrespective of number of scores.
You can always cancel your first score and reinstate it later, even after your second attempt. Given that Business schools do not get to see cancelled score report now, I believe doing so gives you lot of flexibility to showcase your high score in first attempt, without anyone knowing you took the test twice, or any number of time.
You can always reinstate your score at a later point in time by paying an additional fee. Go through the guidelines in MBA.com
https://www.mba.com/exams/gmat/after-the-exam/gmat-scores-and-score-reports/cancelling-reinstating-gmat-scoregempony
Let's say I accepted the score in my first GMAT test but I felt I could do even better, and therefore I retook the test and indeed scored higher. Can I send these 2 scores to 2 separate groups of schools? and will the schools that got my second GMAT score, know my first GMAT score?