The only way to achieve what you're looking for is:
- Modify Android at the firmware level
- Make your app the homescreen replacement.
Option 2 is considerably easier. Basically, you tell Android that your app is the replacement home screen, and then set it as the default on each device. That way, whenever the device is unlocked, your app will be shown, and pressing the home button will only launch your app. This essentially stops the device from opening up any other apps, unless it is done via notifications, which you can take away by making your app full screen. The only possibility left to leave your app now is via recent apps, or a service that launched apps on a device shake or something. You can get around this by making sure that no other app was launched prior to yours, or clearing the recent apps manually. The service can be gotten around by simple not installing any app that does that.
You can look into the default home screen app, which is open source and available at:
https://android.googlesource.com/platform/packages/apps/Launcher2.git