Replacing Old SIte

I cannot figure out how to get rid of the old site that is currently posted and replace with a newly designed site.

1. I have created a new site in a subdirectory of the main site.
2. An old site that I did not create is up and running in a different directory and redirects to the root URL.

I have tried everything I can find to make the new site point to the root URL but I cannot get rid of that old site.
For example:
Old Site Dashboard
Wordpress Address: https://www.root.org/olddirectory
Site Address: https://www.root.org
Goes to old site.

New Site
Wordpress Address: https://www.root.org/newdirectory
Site Address: https://www.root.org
Goes to old site

Old Site:
Wordpress Address: https://www.root.org/newdirectory
Site Address: https://www.root.org/
Automatically logs out and I can’t log back in unless I go to the file manager and manually change the sites back.

And if I put anything other than root.org/newdirectory in both the wordpress and site address fields on the new site dashboard, I get an error message when I try to open the site.

I cannot figure out how to get rid of that old site for anything.
Perhaps there is a way to just overwrite the old files in the original directory with the new files and let it continue to point as it chooses.

Hopefully I’ve explained it where someone can have an understanding of the issue.

Thanks in advance!