The setting to hide the device's number is in the Phone app, tap the menu button, hit Settings, and tap the Supplementary services section. There, IF your carrier supports it, you'll see the Show Caller ID toggle.
Bear in mind that Caller ID info is carrier-dependent, so if your wife's phone isn't set to hide her number but you're still getting 'Private Number' in your caller ID when her number calls, that's on the carrier's side (either the caller's or the receiver's).