Until you get your video, I'll try and talk you through it. That punching motion is alternately pulling the top wing towards you when the kite is sideways to maintain lift and altitude.
Lets start with a normal hover (not inverted). As you slowly counter rotate your wrists to make the kite spin, pull back on the rising wing. When the kite goes 180 (inverted), you will need to be giving brake to maintain altitude. If you are still counter rotating (and you should be), when the other wing rises, pull it back. Not enough and the kite sinks, too much and it rises. This is just like vertical side slides. The wobbles will be not enough or too much of something. Try to do everything as slow as you can to begin with. You'll have time to figure out what the kite needs and what you might be doing wrong. Yeah, it could happen.
Good luck, miss you.