Can the point and shoot do this?
This?
Maybe this?
or perhaps...
Maybe...
Of course, I can't resist at least one..
All different lenses.
The others are correct as to why you're wife's camera appears sharper in 'macro mode' compared to your camera, both wide open. If you want that kind of sharpness, you are going to need a dedicated macro setup. Either an actual macro lens or one of the cobbled setups you'll read about around here. Even then, wide open isn't going to suffice for sharp front to back shots. One thing I don't think I saw mentioned is this. The closer you are to a subject, the smaller the DOF as well.
My general opinion is this. It isn't always Just about being Sharp. It's being able to manipulate Where it's sharp, How sharp, and the overall affect it has on the rest of the photo. It's about color reproduction. It's about getting detail with colors that tend to bleed together, especially on point and shoots (reds and yellows). The bigger your sensor, the better off you are in those respects.
Other people's mileage may and will vary, that's just the way I see it.