Your driving trainer should have you hitching the horse, unhitching, so you know where things go and why. They should teach you what to check to see that things are adjusted, fitted to the horse correctly. Your time spent with trainer is to teach you how to react CORRECTLY in situations that WILL happen out driving. Some horses will need encouraging to go forward, while others are very forward, brave, you just steer them past when encountering new stuff. You need to be carrying whip about all the time, it is your "legs" like the rider has. You touch on the left or right for moving sideways, bending. Whip should have stick and lash long enough to reach the horse shoulder. NO BUTT WHACKING with whip or reins! Totally a movie thing!! Hitting in the rump seems to encourage kicking in some animals, so best to avoid it at all.
I would have my trainer do some "remember this" work with my supposedly trained horses, to see if they do respond well. Some folks call them drivable after only a couple hitchings, horse really does not understand well or respond well to new things when hitched up. We have seen too much of that kind of driving training, people and animals get hurt. Better to do a review of driving, before trying him on your own. Trainers see MANY animals, are much more competent at reading them, responding FAST, correctly, to keep things under control during a review. Think of review as a "tune-up" for the horse, making sure his responses are correct when you issue the directions to him. You both will have a lot more fun that way, he is more dependable to make you confident as his driver.