Here is an option, while it is not exactly what you asked for, it will accomplish most of your goals:
- Create a new folder at the root of your boot drive and name it
PubApplications, duplicate the permissions of the Applications
- Copy (Option Drag) Don't Move all applications that you
want publicly accessible to that folder.
- Copy Don't Move the apps you want in your ~/Applications folder to that folder.
- Rename /Applications to /Applications.bak or /.Applications.bak if you want
Create a symlink in your root folder named Applications, pointing to the Applications folder in your home directory.
ln -s /Users/your_name/Applications /Applications
I am not sure who uses the computer besides you, and I am also not sure exactly what you are trying to accomplish, whether it is to streamline backups, or keep your apps private from others, or if this is simply where you like to install apps.
Note - the above above method will break things for other users if they exist. You could use:
ln -s ~/Applications /Applications
instead of the previous symlink command, although I have had issues with that and you would need to ensure each user had a ~/Applications folder.