Welcome to the forum! I know this has been discussed on here before but I couldn't find it on my first search attempt. What I do with our youngsters is train them almost from the moment they are born to lead well and accept new things. We take them for walks down the road, train them for halter obstacle (trail), and get them used to scary sights (e.g. umbrellas) and sounds (rattling tin cans)(e.g. desensitize them). This includes walking them over bridges, tarps, etc, trotting and whoaing on command, ground tying, turns on forehand and haunches, sidepassing and backing. We also teach them showmanship, which just reinforces the discipline. Taking them to shows will help to, in exposing them to new things. We just started training a new 3 year old to drive and realized she had not gone through our "basic training" so we took a step back and brought her up to where are yearlings are. That helped a whole bunch!
For the mare, I would take her back and start her over, and take her through all the training steps. You might do things a bit different than what she is used to or you may find out she forgot a lot. Don't want to scare you, but it is not unheard of to find out that a supposedly trained to drive horse is not, or else (even worse) had a bad experience. You should be able to tell from her response at each step if she is comfortable with it or not. If she seems fine, you may be able to move along to the next step fairly quickly. I suggest you find a driving trainer who could help you with her, and then carry that knowledge over to the stallion.
Good luck.
