I agree that the wheels could be a little larger, but not much because the shafts will be too high on the pony body. You kind of want the shafts running down the middle of the body, if possible. You can fudge it a little above or below, but to look and work best, mid way on body is your choice.
Has your husband ever held the shafts, while someone climbed in or out of the vehicle? This might be an eye-opener for him, as the weight of shafts changes dramatically when the seated person leans forward or back against the seatback. Puts their feet up on the dashboard! Axle is the pivot point, like the wheelbarrow. Seat postion above the axle can be too forward or too far back, making the moving, seated person change the shaft weight on the pony suddenly as they shift. The more the moving person weighs, the heavier the shafts get on pony back or pull upward on his belly, when that person leans back gets weight behind the axle
Ideally, you want very little shaft weight on the harness, not more than about 10 pounds with passengers in the vehicle. Load is supposed to balance while driving, not heavy or no weight at all. This 10# shaft weight is about the same on a larger horse’s back, or the mini. Sometimes the shaft weight WILL be heavier, like when getting in or out of the cart, stopping or downhill travel. Animal should accept that, then things lighten up on the flat, everyone seated quietly.
You have not mentioned how you plan to use the pony in the long run. Just out fun driving? Maybe do some trails or drive around out in the field? Take the husband and any kids along? Maybe catch a show now and again? I am asking so we have better information about what we recommend to use. Minis are small, and need to have that kept in mind. Road driving with prepared surface of firm gravel is easier to pull on than trails or fields, the arena.
4-wheels have more drag to pull, though no shaft weight on the pony like a cart does. Some styles of wheels seem to dig in more, while others leave almost no tracks on soft ground. So all road driving might work with the bike type tires, light weight for sure! Bike tires have a bad name for bending and rolling the rubber off the wheel when used in places other than the arena. Not designed for the sideways torque carts can give them whe we are out having fun. Other folks have had motorcyle wheels put on their carts for driving on sand, gives a ‘float’ type ride which is not so tiring to pull. They are real happy with the change, say they have no problems with that upgrade in hard use with their carts.
4-wheels do give more room to sit, spread out the load being pulled. You have to learn to turn well with the fold action, carts just follow the horse.
The Glinkowski shown, might come with pnuematic tires as an option, which are getting more common on pleasure vehicles. They do improve the ride, without the loss of tires in field drives or on rough roads. Hubs and spokes are metal and very solid for any kind of driving. They won’t fold!
A friend has the model carriage shown, and it is VERY nice. Pulls quite easily, really almost no weight on flat ground when I moved it around empty. Not any heavier pull than a kids’ type Red Flyer wagon in the yard. She drives a Pair, 34" geldings I think. She has used the vehicle hard, CDE and pleasure showing, it has done a good job for her. However it was NOT INEXPENSIVE, took her some saving up to get it. Quality is excellent in all areas of vehicle, she has been very happy to have it. She says it is even comfortable seating for true ADULT size people, not just children. Many of the mini things are really not adult sized. She has one energizer-bunny mini, who would pull it alone. However with anything except flat ground, her riding alone, very short drive, she thinks it would be too heavy for much driving with her 34" mini as a single. Just works better as a Pair vehicle for her sized animals. Brakes help hold the load on hills, if she has friends along.
Not sure what your budget is, for horse toys. Some prices might scare you if you haven’t been shopping much for the better vehicles. Sometimes you can find used stuff, save a little. Hope the things mentioned, help you with deciding what you want.