Just to add: you only need to set the owner of the instanced scene, not any children the instanced scene has, as their owners will be correctly set. For example, if you are instancing the following scene tree:
Then you only need to set the owner of the Player node when instancing it, as the Health_Bar and Inventory nodes will have their owner correctly set to Player.
(Note: This is from what I remember with saving nodes dynamically in the editor. I'm not 100% if the same applies during runtime)