Since people have already mentioned most of the tricks I could think of, I'll give you an exercise we usually give to the more advance riders, but could work for your kid at a walk. So if your pony is good with crops, give the kid a short crop to hold in between the reins and her thumb (horizontally). So she's holding the crop with both of her hands (so you don't want a crop that is too long and will stick out too much on each sides). Now she had to try and control the horse in that position. I won't prevent her from moving her hands up or down, but it's great to show how to turn and halt without separating the hands/pulling harder with one hand. Like I said, this is a trickier exercise, I've only done it with my more advance students (w/t/c), but you could always try it at a walk and see if it helps.
If all fails, I'm afraid you'll have to be annoying and remind her to fix her hands every time she moves them incorrectly. It'll be very annoying to both you and her, but in the end repetition is key with an 8yo.