Managing screen flow: scenes or layers?

Hi all,
I’m working on a football management videogame and I’m planning the flow between one screen and another. In addition to a central fixed dock with icons for navigation, I intended to divide the game screen into 3 parts:

1 - a larger central one where most of the statistics are displayed (leagues, mail messages, opponent rosters, etc.),
2 - the second, on the left, with the player’s tab (with the ability to minimize it with basic information),
3 - the third, on the right, with the tab of all other “characters” visible in the game (opponents, coaches, etc.).

I’m not sure how to organize the flow between layers and scenes because navigation in the three sections is independent of each other, and using different scenes for certain sections, I fear I might lose visibility in the other two, while using too many layers in the same scene, I fear it might become a nightmare to manage them all together.

How do you think I should organize myself?

I hope I have been clear, thank you!