If you watch herd dynamics, a horse kicks at being driven when they are challenging dominance or exibiting it. Most likely it is a dominance issue and so if you have to act like a psychopath for a bit so be it but you must establish dominance and retain it. Mostly you can just keep insisting on movement until the horse tires of the constant pressure.. however we humans usually tire of the game first. You can also be very extreme in your response to the kick, but you will risk that your horse may truly challenge you and that could be trouble. You could also try something like laying the horse down, but I highly reccommend getting professional help for something like that. Any way you slice it, you are going to have to cause this horse to submit. Any one of a number of approaches will work, you have to determine which one does for you and your horse.
Hmm, just gotta say that the best horse I ever owned kicked on the longe, so we didn't longe. Sounds stupid, but this horse would pack my 15 year old butt over miles of trails alone, bareback, while I did really stupid things most of the time. I think because he was such a big guy that longeing was difficult for him, and I also think he felt threatened by the whip (he would also turn to kick people who entered his stall if they were carrying something). My trainer's suggestion (Max von Bleucher from the Spanish Riding School... RIP) said "so what? Don't longe, just get on" so I did. That was really the coolest horse ever, and unfortunately I lost him at age 8 to colic.