Ben,
SOME pump shotguns are designed to require a slight forward nudge on the forend before the action will unlock. I don't know if the H&R Pardner is designed this way or not. One way to find out is to be sure the gun is completely unloaded, rack the slide to cock the hammer. Then with the safety off, pull the trigger while simultaneously exerting a rearward pressure on the forend. If the slide immediately starts rearward upon the pulling of the trigger, then the gun is not designed to require a slight forward nudge to unlock the action.
Secondly, the thing to do is to see if your wife can operate the gun properly with NO ammo in the gun. If she can hold the gun, dryfire it, and then rack the slide properly with the gun empty, then we know that the gun is functioning well.
If she can successfully work the gun with no ammo in it, then it's a matter of either dealing with the recoil issue or perhaps the shells are sticking in the chamber and she doesn't have the strength to pump the slide. I've seen shells stick so badly in a pump gun's chamber that a grown man couldn't get the slide to work. If the shells are sticking in the chamber, then you can polish the chamber and/or buy some better quality shells which have brass heads instead of steel heads.
So, to sum it up, it's a process of elimination to solve the problem. Do the things in the order I suggested and I think you will quickly find out what the real problem is.