How does UAC work? A.
When an administrator logs in, this version of Windows creates two separate access tokens for the user: the standard user access token and the administrator access token. The standard user access token is the same user information as the administrator access token, but the Windows administrative privileges and SID have been removed. The standard user access token is used to run applications ...
When you register locally, your administrator token is lost. Since you granted access to your instance prior to BUILTIN\Administrators , you are locked out of the instance. With remote authentication, the administrator token is saved and you get access. You would gain access if you selected RunAs \ Administrator at application startup (SSMS?).
The solution is to explicitly give you access:
create login [domain\you] from windows; exec sp_addsrvrolemember 'domain\you','sysadmin';
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