"This is the man whose brother has two children."
Translation:Dette er manden hvis bror har to børn.
"Dette" is correct. I can't exactly explain why, but it seems to me that it might have something to do with "dette" not referring to "manden", but to "that general thing over there". Nonetheless, "dette" is correct.
Source: Native speaker
I see. Sort of like how German uses "das" in the same context, regardless of gender.
Might have to do with danish once having three genders; male, female and neuter. We lost the male gender sometime in the past 1000 years. I don't know if that's true though.
How lucky that the danish people did not go extinct as a consequence of that lost. ;))