This is just my opinion and for whatever it is worth, I agree with your Mom. You shoot it, you eat it.

Unless you are killing critters because they are a destructive nuisance, like the rabbits and chipmunks on my property, the animals you go out of your way to hunt and kill deserve to be used to their fullest.

If you want something that is more challenging to shoot than just paper, balloons are fun. Tie them to a target frame and blast away. On a windy day this can be very challenging. Balloons have the advantage of being cheap targets that build up your marksmanship with no guilt!

Are your scope rings loose? How about their attachment to the rifle? From what you are describing you have

1. Loose rings
2. A scope problem - a possibility with a cheap scope
3. Breathing/trigger control issues.
4. A receiver that is seriously out of alignment - not very likely.

All the best,
~Robert