I think the in-hand training will only HELP her in the cart. I do in-hand work with Princess in her harness (or a surcingle), doing shoulder in and "leg" yields. I would love to work her up to high level moves like levade, which I think she would be capable of, but just don't have the time. But any exercises like shoulder in and leg yield should make your mini more flexible and easier to get on the bit when driving.
Princess also does in-hand jumping (see my signature, which doesn't include that she does ADS driving shows too). Someone just asked about that so you might want to search for that thread. I don't do any jumping in the winter when the ground is frozen but if you have an indoor you would be all set. After we get ours used to walking and trotting ground poles (at a young age) when they are ready to start to jump (age 3) we usually start them over a downed dead tree, which we always seem to have in our pasture. They can't duck out and they can't knock it down. Actually, they will have all jumped it already as babies!! Then we do a low cross rail to teach them to jump the center of the jump, then go from there - slowly!! Key things for us are having the horse trot (I am too old to have the horse canter) next to you and follow your lead, never getting ahead or behind and making smooth turns. If they start to rush the jumps, then the jump itself becomes a reward for trotting nice and steady. Ours all love to jump and they wait impatiently when they see the others going over the course in our back yard!