Ok, so yes you have records of his being european, and yes the records showed him to be white.
Say he was full white...If you dont' know what HIS wife was, then as you said, you can't know what their daughter was..(daughter being the half brother's wife)
If the daughter was half white and half Black, and her husband was Black, then the children would be 3/4 Black, and not Mulatto in the sense of Mulatto being half white and half Black...
If that's the case, then I don't know why the woman (half brother's wife) wasn't classified as Mulatto and the rest of the family Black.
Are you positive your g-grandfather knew about the white father of his half brother's wife? I'd like to think that he didn't know, rather than that he lied about her being Black rather than Mulatto...For the life of me, I can't see any purpose for him or anyone to *lie* about whether someone is Black or Mulatto, for that matter...