I tow a 2013 Chev Equinox and have had issues with charging the battery. There are some posts on the problem and fuses you may want to read. Start with this one. https://www.irv2.com/forums/f85/2013...ng-541683.html
I attached the GM service bulletin for your reference.
I did solve my charging problem by replacing the light gauge Roadmaster pigtail, the small round 6 pin plug on the car end and improving wiring on both sides of the plugs to increase ampacity.