When you connect to the host, are you using a login that exists on that Mac, or some other method.
If you log in with an account that is on the host, you should have all the access that user has.
You would need to use the Sharing System Preferences (File Sharing) to give the user you are using to connect the access you want them to have.
File Sharing in Finder will initially try to log in with the credentials of the user account. If the account on the client Mac has the same credentials on the host Mac, but not access to the drive, then you would need to provide the desired access in File Sharing. Or, after it connects, click Connect As… and enter the necessary credentials.