Among Dominicans, I would guess fewer than 5% use a private car. Motorbikes are far more common and the vast majority of the population uses mass transit of some kind. It is cheap and convenient. I would not reccommend driving for anyone who has not been in the country for at least six months and has had several years experience driving elsewhere. I wouldn't drive there myself.
For short trips, people take motoconchos, for medium trips they take publicos or Gua guas and for bigger trips, they take buses. Don't let your daughter take a moto concho on a highway because many drivers will go extra fast to try to impress her. In a city, $2-$3 a day should be plenty to cover taxi/bus fares.
Transportation in the Dominican Republic
Motorbike taxis are call
motoconchos, private taxis with other passengers are called
publicos, and the minivans are call
guaguas.
It takes a bit of time to learn what to pay but it is not pricey once you have some basic Spanish.