Hi Takatso, welcome to sevenforums. As I read you post, it looks like you are logged into your domain joined PC as a domain user is this correct? If so, your PC will be treated as acting as a part of the domain. If you then try and connect to another pc at home, there will be a problem as your home pc is not recognised by the domain pc as part of the domain. You should set yourself up a user account on the domain pc whilst it is NOT connected to the domain, login to the new account whilst not on the domain and then try sharing the folders with the non-domain pc.
No, your does not have access on the home computer as they are part of the domain and not the homegroup.