I would skip the riding while driving part, and just get a cart or buggy that lets you and DD sit together! Part of the fun in Driving, is that you can take passengers and CONVERSE without having to keep tweaking the ridden horses to stay even, not bite or make ugly faces at the other horse, etc.
You will want to practice STOP and STAND, fairly often, so horse is good about waiting for command to walk forward. This is one of the VERY important parts in a good Driving horse, standing still for long times. Some horses have a timer in their head, will give you 30 seconds, or even 2 minutes, but after that, they want to GO FORWARD strongly!!
If you get him a harness, go for a wider saddle, 4", to take the weight of cart shafts. Carts (cart always means a 2-wheeler) balance on the shafts on the harness saddle of the horse. So any passenger movement does affect the horse, and a wider saddle allows weight to spread a bit on a larger area of the body. Harness saddle NEEDS a saddle tree inside, to prevent weight on horse spine. Try bending the harness saddle by pushing gently on both side flaps, it shouldn’t fold in half if there is a tree inside. There are quite a few used harnesses out and around, so you can find things for less than new prices. Get his measurements and carry them so you know exactly what will fit as you shop. You want the best (perfect is not always possible) fit to fall into the middle hole of each buckle, which will leave holes to let out or take up as horse gets fit or fat.
Not sure how far you are from Lancaster PA, but the big Martin’s Carriage Sale is coming up at the end of April. Could be worth the trip to learn what is available, what prices are doing, or even buy stuff to take home with you. You will see stuff going for record prices and huge bargin sale prices. It is ALWAYS an amazing sale, sure covers the whole realm of Driving horse equipment!