I always find it helpful to lunge a little bit first, to reinforce the transition to work. How far and long did you ride?
Most horses figure out the rate thing after they get really tired a few times, but to get there, you have to do the time. I have never had an Arabian get sullen about going the distance.
On the jiggy thing, I just do circles until I get a walk, then just let the reins loose and walk on. If they start to jig, circle until you get the walk, the loosen the reins, and walk. If it is a certain direction, like back to the barn or trailer, I will do the same, but either go past it, and insist on obedience coming back again, or WORK at the trailer/barn even harder, so it is not the REST that they expected.
You have to have TIME to teach this, you cannot rush it, or have a deadline, so start early in the day.