Do you actually have a domain at home, or are you using workgroups?
Just a workgroup.
If it's a workgroup, I don't think you can use AD for other desktops. With SSRS you can get around it by having a user with the same username and password, however, can a SSMS I'm pretty confident in saying it uses the SID of the user, which'll be different on the 2 PC's (even if they have the same username and password).
You'll likely need to use SQL Authentication to connect from other environments other than the Host Machine. (Of course, I'm happy for someone to prove me wrong).
Thom is right, you will need to use SQL Authentication and ensure that the sever is configured for remote connections. If you are using Windows Firewall you will also need to allow incoming connections on the port, which if it is default will be 1433. Ensure also that the browser service is installed and running, I think Thom was going to mention that too.