As long as the side bar is showing, opening a subfolder will always take over the view of the same Finder/folder window.
To prevent that, with the folder highlighted, press Command+Option+T to hide the sidebar. Now when you double click any subfolders, they'll open in their own window, and so will any deeper folders as they will all open with the sidebar already hidden.
To make this the default (as much as possible), create a new folder and set it up they way you would prefer. I always use List mode and the side bar hidden. When you have it set, right click on the folder and choose Show Options. At the bottom of the palette, click Use as Defaults. Close the window.
In the future, all new folders you create will have these attributes. All except for any created directly on the desktop, which for some reason, are still created with the sidebar as visible.
Hopefully, I got these keyboard commands right. On my iPad at the moment.