Okay, so I come across said uncle, and he turns to face me. I'd expect some sort of conversation to happen...but nothing happens. I can't just hand him the gift, either.
Is this some sort of glitch?

Hi,
Have you tried pressing the 'use' key ?

Postal 2 doesn't have a "Use" key per se, unless you mean the one for items.
And, yes, I did try pressing the "use item" and "drop item" keys.

Ok then.
How about shooting Dave ? That's what i would try next :)

Sounds like a glitch. I remember Uncle Dave talking immediately once you found him.
Do you have a slightly older save file, and maybe you could try again?

W walk up to Dave and give him the
present. Press the "use" key. Watch the cutscene and get ready to
fight, since heavily armored ATF agent are storming the house.
Now everybody is after, both the police and your uncle Dave.
Backtrack through the building and climb out on the roof.
Run away from the building, following the road.
At the loading zone, the fat police sergent will be there with a R. launcher,
kill him and
exit the area. Mission accomplished!
now if that's not happening you should indeed try again with an older save game amigo

Okay, I don't know what happened this time other than me going out of the area and back in again, but the conversation with Dave started this time, and I could give him the gift. After that, the tank that crashed into the house backs out and the ATF starts swarming in.
Maybe I won't have to level-skip after all.

great , glad it worked :)

Postal 2 is a bit finickity about where you stand sometimes.