Oxford is at least 90 minutes to Memphis any way you slice it. The freeway portion of I22 ends just past Byhalia and turns into US78. Traffic slows down well outside of the city around the freight terminal. We go to Memphis that way, though we are not from Oxford. It's about the same distance time-wise from Grenada, with the convenience factor of interstate 55 the whole way. All the shopping she's likely to enjoy will be on the northeast side (Germantown), so she's going to be driving a good ways across town in either case. Clearly, this is all relative coming from Dallas given the traffic and sprawl you're used to, but can get old quick.
Oxford has higher real estate prices and decent public schools, but Grenada is cheaper and you'll likely want private schools, so that's the biggest trade-off to me. Oxford has the edge for "social" stuff, but that's nonexistent from May through August, except maybe youth sports.
If you've never been to Mississippi, then you're in for an adjustment, but not in a bad way. I've lived here for nearly 15 years and have loved it. With the exception of the Delta, there's lots of similarities to East Texas, culturally speaking. Just enjoy the different opportunities to explore. Take a couple of weekends amd explore the Delta. Drive to Natchez and see the balloon race in October. Obviously see football games - Starkville and Tuscaloosa aren't all that far. You'd be in a bbq black hole, but Memphis is close enough. Hunting and fishing are especially good here. There's lots to see and do if you're willing to get out and see it.