I have small hands too and have less strength braking from the hoods. At first I was uncomfortable with braking from the drops and I did what Dirt Diva said practiced on flats or easy downhills. Using my drops on long downhills has become so natural to me that I don't even think about it anymore and now being on the hoods is more scary.

For me it was also a matter of getting the correct fitting bar. Ideally, I need a 34cm handlebar bar but had 38 cm on my bike. Because my bar was so wide my elbows angled out instead of straight and also required my hands to angle at the wrist. I'm sure this put a lot of stress on my arm muscles because braking from the hoods or drops was painful on long descents.

Getting the correct width bar with drops that put me closer to the brake levers made all the difference in the world for me, no more odd angle of the arms and wrist. I still brake from the hoods on flats and for quick stops.

When I built my last bike my LBS wanted me to use Shimano levers instead of Campy. My fear was the Shimano levers were to bulky to brake from the hoods. From what I'm reading here I'm so glad that I stayed with Campy.

If they haven't done it have your bike shop measure your shoulders and verify that the width of your bars are correct.