Wendy,
This is indeed very strange. If it was only one hand I would say he was bitten by something. Which would give you localized swelling. But for it to be both hands, but not the fingers, is almost against what anatomy says would happen.
However, you can get swelling within the wrists (the intercarpal joints), that would involve what most people feel is the proximal hands. This could also cause some swelling in the tissues adjacent to the wrists (ie the hands), and not involve the fingers.
Gout can affect the wrists, without it affecting other joints. There are also a whole host of inflammatory arthropathies that affect the wrists.
If the symptoms do not abate soon, he should probably be seen by his physician (or a rheumatologist), while the hands/wrists are swollen. Aspiration of the edema/effusion can often give you a diagnosis.
Hope your father feels better soon. Good luck.