I am not sure if this is the right area to put this in but if I apply to the college (in this case- the University of Houston) with one ACT score, apply to the scholarship (before the 2nd ACT score comes out), then have the ACT score for the 2nd ACT sent to the school, will they look at both, the highest one, or the 2nd one? Or is this a case-by-case situation? Thank you in advance!
There is no one answer for that among colleges, and there is often even no one answer within a college because it may depend on particular scholarship you are seeking. Some colleges make most or all scholarship decisions after admission decisions are made and use later received test scores for that. Some have priority dates earlier than the regular end date by which you must apply for admission if you want to be considered for a scholarship, and use whatever test scores are submitted by the priority date.
University of Houston, at least for university funded merit scholarships that incoming freshman can get, follows that priority date system. You must apply to the university and submit all supporting materials, including any test scores you want the college to consider, by Nov 15. Test scores received after that date will not be considered. See http://www.uh.edu/financial/undergraduate/types-aid/scholarships/