Cannot access ReadyNAS 104 shares from PCs

It's simpler to start with the home laptop, since there are no domain-level security policies in place on that machine (which are controlled by your employer, and not by you).

Start by creating Windows credentials for the NAS in the PC's credential manager that has the desired NAS username (admin) and the associated password.  Windows treats the hostname and the IP address as two different machines, so I recommend creating credentials for both.  The username/password can be different in the two credentials (and sometimes that is useful).  Keep in mind that Windows only allows one credential to be used with a server at any given time (and it will keep connections open even after you close the file manager window).  There is some information on accessing the credential manager here: https://support.microsoft.com/en-us/help/4026814/windows-accessing-credential-manager. 

After the credentials are entered, reboot the home PC and confirm that your access issue is resolved.  When you get that working properly, try doing the same thing on your work laptop.

It is possible that the entering the credential won't be enough on the work laptop.  Your employer might have a domain-specific security policy in place to prevent SMB access when you are not connected to the corporate network.  My own employer has a similar policy - in my case I need to be connected to the corporate VPN in order to use SMB (but once I do that, I can connect to my NAS).  It there is a security policy that prevents access, you could try installing the Windows NFS client on that laptop, and see if NFS is allowed.  If it isn't, you might need to fall back to FTP (using an FTP client such as FileZilla or WinSCP).