DUDU-Meng Even if this is the case as you describe it, and even if we need to start firstly TomTom in full screen mode, once we go back to the home screen with the widgets, TomTom is forced closed and starts again from zero...
 
Your system has its pros and cons. I like the speed and the fluidity but to me you have modified too much the original Android OS by adding your own software bricks on top. That's cool no problem with that, however here you are seeing the matter from your personal point of view. Each app developer of course takes into consideration some standards and norms that Android applies. So every app can work correctly with these standards.
If you decide as DUDU company to customise heavily the android OS to offer different or additional functionalities, to my understanding it is you as DUDU that has to make sure that your system is compatible with the standard Android OS norms and development rules... For instance if you decide to add a toolbar or a widget for PiP, make sure to check that everything works first and if not either remove the support for this app or make sure to resolve the issues so that you can pass the correct arguments to the app when changing from widget to full-screen mode and vice versa.
For Cosmote TV that I mentioned also that does not allow me to play the Greek TV channels due to modified permissions of Android in DUDU OS I didn't get any comment from you. And of course a reply like "you should contact Cosmote developers for that" would not be valid, as the app is working correctly on all my other devices except from DUDU OS...