On open road, SUV hesitates quite a lot. Like, insufficient fuel compression

The first thing I would like to suggest is that warning lights do not need to be present to perform a diagnosis. The hardest part of most any diagnosis is the lack of ability to duplicate the concern. As long as the problem is happening, a good technician will be able to determine the source of the problem. Which engine do you have? The 3.0L V6 was not offered in 2013. The best thing to do would be to have a local technician road test with you to see what you are experiencing and then proceed from there towards a diagnostic procedure.