There are TWO forms of recoil - ACTUAL, which is a mathematical calculation based on weight of the gun, velocity of the payload and the mass of the ejecta (shot/wad/powder)
Then there is PERCEIVED, or FELT recoil which is a function of gun fit, softening agents like pads and action types. Using a good recoil pad, a gas gun, and one that fits will let him FEEL less recoil.
Actual recoil is reduced by using the heaviest gun (typically from 8-12#), with the lightest load (typically 7/8 in 12 gauge)
A pump gun is one of the WORST guns to use because they tend to be very light and they never seem to perfectly fit anyone.
Next time out, talk to some of the the veterans at your club and see if your dad can borrow, or at least rent, some various trap guns and have him try them. ask them what they use and why they use those particular guns. They don't have to be $15,000 guns, but they DO need to fit.
Good luck on getting this resolved...........