You've gotten some great advice here and since I still can't see the picture (viewing from work) I won't comment personally, but I did want to discuss a couple things Chamomile said. Overall her advice is excellent and quite accurate; I just want to make sure a couple points are clarified.
Chamomile said:
As for her struggling with you in the cart, she does need to be in shape, and learn to pull with her hind end and not her back. The way you do this is to drive, drive, drive!
Driving by itself is enough to condition her for pulling the cart. Learning to drive CORRECTLY, however, meaning she's pushing from her hindquarters instead of pulling with her chest, takes driving
correctly for many many hours. Perfect practice makes perfect!
Chamomile said:
You ask her to move forward and never pull on her mouth when she does so. Always encourage forward movement. If she breaks gait, wait a few strides, then lightly ask her to shift into a downward transition. The lighter you are on her mouth, the better. What kind of bit are you using?
I don't disagree with Mindy here, but I'm concerned that many new drivers will take this to mean that you shouldn't touch your horse's mouth. I already see so many drivers slapping along like they're in a Western movie with their reins draped and the horse up there clueless, I'd hate to see any more!
When you ride, the horse has your weight, seat, legs and reins to tell him what you plan to do. When you make a turn he feels your shift in weight as you look the way you plan to go, your seat hopefully lightens and collects him, and your leg gives the cue. He can afford to go on a loose rein because of all that other input and if he gets scared he knows you're right there with him through the feel of your body on his back and because he can see you. When you're driving your horse is up there all alone. He's got blinkers on so the only way he knows he's got someone he can trust with him is through your voice and your hands on the lines. It's important that you hold that connection with him through the reins, a constant soft contact that "holds his hand" and lets him know you're together. Mindy's right that you don't ever pull on his mouth, or yank him or otherwise break that trust. Lighter is better, but that's lighter as in more elastic, softer, gentler, smoother- not lighter as in less contact. As your horse gets used to holding correct contact he'll actually "follow the bit down" if you give him rein, seeking that friendly feel in his mouth.
With a green horse like yours, yes, by all means feed her some rein if she's reluctant to make an upward transition. However that is only a brief phase as she gets the idea that going forward is what you want. Once she understands that you should gradually come to hold a similar level of contact through the transition as you did at the walk and she'll learn to push up under herself and round into the frame you've built for her (always soft and yielding, not a brick wall she hits!) and she'll begin to move correctly and with more energy. It's like trying to chase a riding horse into a canter- they string out and sort of fall into the next gait quite roughly and with a complete lack of grace. If you collect the horse into your quiet hands and
lift them into the canter with your seat and legs (or in this case voice) they will round up, elevate the forehand and step lightly into the next gait. This is not only much prettier, but much better for the horse's body and mind.
Mindy is absolutely right about how to handle a break in pace. Don't get hard and angry and snatch at the horse's mouth but instead handle it quietly and simply request firmly that she drops back to the previous gait and praise her when she does. When you don't make a big deal of it neither will the horse and she'll soon stop trying that as she comes to understand you want her to remain at the same pace. Remember also that a green horse will try to break pace both upward and downward when he or she is tired. They may try to break to a walk, but breaking to a canter is also a way of trying to give their muscles a break. Even experienced horses will do this in deep footing because a canter gives more of a lunging motion which helps drag the cart along. Watch out for this and if the horse starts breaking to a canter for a stride every couple of strides you should give him a break. Driving is hard work!
Genie said:
You have a nice thick pad on it, which I do as well, because my guy doesn't like feeling the "slapping" movement on his chest on rough terrain.
If your harness is adjusted correctly, the breastcollar should never slap the horse in any way. It should be constantly against his chest and swinging easily forward with the movement of the shoulder thanks to the singletree.
Gracie, just give your mare plenty of time to get used to the work you're asking of her. It will help if she's also being round-penned or lunged or treadmilled or otherwise conditioned outside of driving as then her wind and propulsive muscles will be getting stronger on their own instead of her body trying to deal with everything at once when she's in harness. Cross-training is very important!
Enjoy your driving.
Leia