You have the NTFS security permissions set incorrectly on your domain files/folders. What server software version are you running?
First place to check is share permissions. To keep it simple, set the share permission to Everyone Full Control. You then restrict access by using NTFS. Basically in a small company (you said you were in mixed domain and workgroup), I would give administrators full control, system full control, and then select which security groups should have other rights to the files/folders.