I\'ve read a lot of documentation and other posts about closing other apps. I know the documentation says Android isn\'t designed that way. Android wants to hibernate an app
What you said is perfectly possible. Just get the ActivityManager system service and then use .restartPackage() (deprecated) or .killBackgroundProcesses().
ActivityManager activityManager = (ActivityManager) context.getSystemService("activity");
activityManager.restartPackage(packageName);
You will need:
<uses-permission android:name="android.permission.RESTART_PACKAGES" />
<uses-permission android:name="android.permission.KILL_BACKGROUND_PROCESSES" />