^^Agree with the post by Ace. Split reins are the very best thing ever in a situation like this (for a western rider anyway, I don't know that I could juggle a whip along with the reins LOL). Since she has already shown that she is perfectly willing to sull up, I would be relatively quick with her force progression. I would squeeze, bump, then whip...hard. When she's going the speed you want, just sit quiet. If she goes to slowing down as soon as you let off the pressure, squeeze then whip again.
Every time she slows down without you cueing for it, be a little more aggressive with correcting her. When you are able to get 4-5 strides of your chosen gait out of her without having to push, then stop and let her stand and catch her breath for a few minutes. If it's been a long day and you've been working her for quite a while, that would be an excellent time to get off, lead her back to the barn, and call it a day.