To the op,
1st follow everyones advice here.
2nd, spotting takes work, unfortunately peels are something you can't really "work" on because they happen seldom.
however all you can do is try to spot them and be in the right location. So at meets and during meet run through when anxiety and energy is at it peak, I stand close to the low bar with both hands ready, (in other words, don't put them behind your back, or on your knees,Like I have seen). use the hand that is closest to the high bar to follow the swing through, (in other words swing it with the child, like you are magically lifting the child with your hand under them without touching them, hand should be at least a foot away and not close to the gymnast). That is your primary catching arm, usually when a child comes off they will go kind of flat but leading with the head a bit, so that arm that is already extended will end up on chest/ stomach, hips and the other arm will will grab whatever. If the child rotates completely head first, your arm is still in the best position and you will bear hug the kid like catching a lawn dart. If the child has a huge swing, (like some of my kids go way above horizontal) I stand right under the low bar facing sideways (like a hockey goalie) , ready to catch on either side, or slow momentum as they land on the low bar. (SLOW) IF you catch them, great and super job, if not then at least you tried and that is all that can be expected.
In workouts, we use extra matting so I can do other things.