The problem is you can’t use windows authentication if you are not on the same domain. SSMS wants to pass your current windows credentials which, if you are not on the same domain, are not the correct ones. There’s a solution. It is (syntax shows SSMS 2008):
runas /netonly /user:northamerica\jnixon "C:\Program Files\Microsoft SQL Server\100\Tools\Binn\VSShell\Common7\IDE\Ssms.exe"