so you will not have any problem to do so. you leave the st dgo airport and where you hit the highway you will see the big signs towards san pedro/la romana, that's your direction. when reaching san pedro don't leave the highway unless you want to do something in san pedro, stay on the highway which makes a turn around san pedro ending at a left/right crossing, your turn is to the left(to your right you would enter san pedro from the eastside). from now on you stay on exactly that road, it will bring you automatically to La Romana, for food and drinks or bathroom you will find a bunch of spots to stop right at that road, no need to leave your route or such. once you reached la romana you will arrive at a big crossing, traffic lights on (the onew which count the seconds til green/red in big numbers on a screen),
here you turn right towards higey(big signs before the crossing show that you have to turn right for higuey, so no prob here), from here on you stay on that road, it will bring you throu an other part of la romana, no need for any turn or such, and when finally leaving la romana the road devides in a lane which leads half to the right and a lane which leads half to the left uphill, signs Higuey are here also present for your left turn towards Higuey. you stay on this road for around 35 minutes without the need to any turn or such, then an other point where the road devides left/right, the so named crossing of Bayahibe, your turn is to the left(signs indicate also here left Higuey), after an other while the same kind of deviding the road left/right, the so called crossing of Yuma, also here signs are on indicating your left turn towards Higuey. so now you enter Higuey and you stay on that mainroad, here you reach a point which is for a newcomer to Higuey maybe not so clear to turn, you see to your right a big gas station and right there the road offers to go on (bit right) or to make a light move towards the left, you take the left and follow that road, you will pass the Basilica(basilica will show up on your left side of the road, you go on straight there driving along the basilica property which alsways has to stay on your left side) until the ropad ends, only left or right turn possible, it is a traffic light,
signs are also up there indicating Bavaro/Punta Cana to the right, so make your right turn and stay on that road leaving Higuey until you are in the middle of La Otra Banda, here you find a crossing with big signs on indicating the turn to the right for Bavaro/Punta Cana, so you turn right and you are on your way to Bavaro/Punta Cana. after around 25-30 minutes you reach Veron, located left and right of that road, a straight on, so go on until you reach the crossing of Veron(big Shell Gas Station on the right side).
from here on it depends on where in Bavaro/Punta Caan you want to drive to, so just name me your detailed final destin on the east and i will give you a driving description for that last part of the way, too.
hope that helps and doesn't sound too complicated, it really isn't difficult, but i am not that good of a way description writer.
have fun
Mike