Yes a road bike will be faster. HOWEVER, you did not say how much you or these ladies weigh.
There is a direct correlation between how much you weigh and how much energy it takes to climb x feet. The formula is:
Work = Mass * gravitational constant * height.
Work is measured in joules, and is Power * Time. Power is watts. So say you weigh 250, and the ladies half of that, 125. This means that it takes the ladies half the amount of work to climb that hill. In order for you to match their speed you need to put out twice the amount of wattage.
As an uber clyde at 380 pounds I have it even worse, since I'm 3-4x heavier than almost everyone I know. I will always get dropped on hills until I lose this weight, no matter what kind of bike I have. It's a fact of life.
I highly recommend road bikes, but don't have the expectation that it will automatically make you an amazing hill climber. Here in the clydes forum, losing our excess weight will always be an easier and cheaper way to gain significant speed.