Lombardo is correct re driving times and his descriptions of Myrtle and the Outer Banks.

Personally, assuming I'm staying in Raleigh/Durham Friday night, I would do this: 1) take Ma to High Point to shop Saturday; 2) Drive from High Point to Wilmington (about 4.5 hours from High Point, right down I-40) Saturday after she's done shopping; 3) stay in Wilmington Saturday and Sunday nights; and 4) drive from Wilmington to RDU Monday mid-morning (I would allow 3 hours to get from Wilmington to RDU).

While you will definitely backtrack, your mother will get her furniture fix and you'll get a better beach experience than Myrtle with less overall driving on better roads. Wilmington is adjacent to Wrightsville Beach and close to other nice NC beaches like Carolina Beach and Kure Beach. These beaches definitely don't have the rustic feel of the Outer Banks, but they're definitely a cut above Myrtle.

Also, early October is absolutely the best time of year in NC weather-wise in my opinion. The beaches won't be nearly as crowded as in the summer, too, and you won't be looking at peak rates for hotels, etc., on the coast. Don't count on swimming in the ocean though.

Hope this helps. Enjoy NC!