Actually, that's an H & R model 732 Pocket Pistol chambered for the .32 cartridge. Look at the cartridges in the photo - they have center-fire primers. Nobody makes center-fire ammunition for handguns in .22 caliber....it's all rim fire ammo.
Down at the gun club, I've seen and handled my share of H & R's. Yes, they're inexpensive, but that doesn't necessarily equal poor quality. It sounds like the problem with your dad's gun was likely the advancing pawl became bent or otherwise damaged. This means that after the cylinder turned, the cartridge was not perfectly lined up with the barrel for the next shot. And the bullet got bits of it shaved off when entering the forcing cone of the barrel, where they then flew back and into your hand. Ouch!