In negation ('Nie pamiętamy naszego wujka') it will be genitive.
Cases (and gender).
"nasze" is either Nominative or Accusative, either neuter or not masculine-personal plural.
"naszego" is either Genitive (masculine or neuter) or Accusative (masculine animate).
So, as "pamiętać" takes Accusative: "My pamiętamy naszego wujka" (masculine animate), but "My pamiętamy nasze dziecko" (neuter) and "My pamiętamy nasze córki" (not masculine-personal plural).
"We are remembering our uncle" is flagged up as incorrect, but i think that pamiętać is a present continuous verb. I perhaps tend to be overly-specific in my English answers but I find these a helpful parallel, from a learning point of view, when thinking of the polish perfective and imperfective equivalents.
Unless I misunderstand "remembering", no it's not. "pamiętamy" is simply stating that... well, that we do remember him. We haven't forgotten him.
If we are thinking about him 'actively', reminding ourselves things and memories connected with him, that's "wspominamy".