We have a greedy grass-snatcher. I would not consider a poke with the elbow in the chest out of line at all! I usually opt for the toe of the boot to the muzzle (not hard, but quick, almost like the horse didn't realize your toe was there when he reached down for grass, and is surprised by it all). When we first got him, my daughter would not lead him into the indoor because he was difficult to control and kept yanking the lead away to eat grass. With consistent correction, she is now able to walk him across a lawn easily. But it took a few jabs and boots to the nose!
In my personal opinion, you are over-reacting and need to be more assertive with this pony because if it tries to take advantage of a groom that knows it, your 8 year old will not be able to do anything with it. I know it's hard to teach kids to be assertive, but it is actually very empowering once they realize they can make this 1000 lb animal mind its manners on the ground, as well as in the saddle.
What I would consider abuse: whipping, punishing using physical force (the difference between a correction and a punishment is all in the timing), and continuing the correction after the behavior has ended. The right way to do it is with a correction, then moving on like nothing happened. Yes, the pony may be surprised. But it's not from pain, just from realizing they're going to have to re-think their plan of running over you.