While tuition to NC public schools are cheap- room and board is not. People often ignore that. That’s why so many kids flee campus the second year. There also is tuition structure that really forces you to max out as many credits as you can each semester- which is not always a good thing if you are in a challenging major.
There is a lot of brainwashing that NC kids need to stay in NC. Up until this year UNC system has not been kind with AP credit, and in the case of IB- basically giving no credit. We found it was cheaper to leave for certain schools. A lot of public universities in NC have invested little money in dorms- UNC-CH has some awful dorms and yet they charge a ridiculous amount.
The OP needs to compare programs, tuition structure, room and board. The family has raised the student on Auburn athletics, it doesn’t seem that they are completely opposed to the school, rather they like the prestige of UNC. Maybe if the OP re-looks at both they might end up seeing things that would sway them back into mom’s direction maybe not- but these would be the things I would bring up with parents.