When i first read this thread, i thought i missed something, lol!
When i teach my horses for Halter/Showmanship, i teach them to lead off of my body. As soon as they see me tip my shoulder and i put a slight bounce in my step, they pick up the trot. I'll have to get a video of it. I never used a whip =)
Miakoda is having issues with keeping with me, and what i do for her is lightly pull the lead, asking her to join me. If she doesn't I "kiss-kiss" and lightly pull again. If i don't get it that time either, i use the excess leadrope i have folded in my left hand, and lightly wisk it behind me where it grazes her side. In most cases, i've found this to be a good routine. Ask once, then demand =) A folded leadrope is a pretty good tool, plus, its less to carry. Sometimes I dont always have a whip on hand, but i ALWAYS have a lead rope =)
Once they figure it out, i can train them to just cue off the kiss, then the tug, then the shoulder. It just takes time, consistency, and patience!
I usually have my horses responsive to pressure on their sides before I train them to trot in hand though ^^