RE: backyard archery practice.....gone wrong...
Sounds to me like you have a VERY unsafe place to shoot and honestly, you should not be shooting there. Regardless of draw/miss-fire accidents, you can get a bounce off the target top or anything else. Haveing ANYTHING like what you describe within probably 100 yards, not feet, yards, behind the target makes it 100% unsafe.
the neighbor has a right to be pissed. You should not be shooting in the area and direction you are shooting. Not all yards are setup for shooting, in fact most are not. Join a club or find a safe place to shoot.