I suppose this applies more to lazy school horses than stubborn ones who are messing around, but my instructor tells me to be very, very quick with my reinforcements. If they don't respond to a squeeze, immediately give a kick. If they don't respond to that, immediately use the crop and leg at once. If you don't get a good enough response, slow them back down, do it again. Don't just keep kicking or they'll learn that they can get away with doing not very much while you hammer at their sides. If it doesn't work, you start from the beginning again, so they know there's no avoiding listening to you. My instructor tells me I need to be much faster with my reinforcement - it's got to follow up the leg aids immediately if the horse is going to get the message.
My instructors are also very, very big on transition work between all gaits to keep the horse responsive and paying attention.
Also, as a weakling, I don't really use my crop hard enough for the horse to pay attention to it. One instructor has me pass both reins into one hand, turn the crop around (so you're holding it kind of like a magic wand) and then I can give a good strong pop with it before turning it back and taking up both reins again.
If you believe everything you read, better not read.