Yes, visit your cousin and spend time at the UNC campus. Chapel Hill is an awesome college town, walkable which you like, Big time D1 sports and great academics. These students will be your peers academically, less so at Auburn. If you ultimately want to pursue engineering after Freshman year you could always transfer to say NC State.
I would think long and hard about choosing Auburn over UNC-Chapel Hill. I completely understand where your mother is coming from. With that said, YOU are the one spending 4 years of your young life attending undergrad college so you have to be 100% committed to your choice.
Good luck, let us know how it goes…