First of all, how busy are these roads that you plan on taking the pony on? Country roads with only a few vehicles or pretty busy road? I would not take take him out on busy roads until he is confident on country roads and does not mind vehicles. Are you going to be riding the pony on the road or your daughter? Or are you just riding him to do the training?
This is how I did it with my horse when we first started out and she was nervous around the roads and cars. Start out riding in the ditches alongside the road. Try not to go in the fields--especially during the spring after they've planted--unless you've asked the farmers and they are okay with it. Stay relaxed but aware of your surroundings. When you hear or see a car coming on, stop the pony and turn him so he can see the car coming. I especially had to do this because my mare only had one eye so I had to make sure she saw the vehicle and didn't freak out. If the pony is staying calm, you can take both reins in one hand and stroke his neck and praise him in soothing tones. If he's starting to get anxious, don't freak out but keep both hands on the reins and talk to him.
If the car is going to fast for you, try waving your hand in the air to get the driver's attention. They usually will slow down thinking you need to ask them something. I'm sorry to say there is no way really of preventing the stupid people who honk their horns while you're riding. Sadly, they usually get a kick out of seeing how the horse will react.
Eventually if your pony is handing the ditches well, you can move up to the road. Horseback riders do have the right of way. It is helpful to ride on the opposite direction of travel on the road so that way you can ride towards oncoming traffic and drivers coming up behind you already have space to get over.
WEAR A HELMET!!
I hope this helps! :)
I also forgot to add, don't trot on the pavement for very long because it is very jarring on the pony's hooves and legs.
Opportunity is missed by most people because it is dressed in overalls and looks like work. ~Thomas Edison