My husband, our three children and I were at DC last August in the rain. If there is lightning sighted (which there was), not only do they stop the dolphin swim, but everyone has to get out of the water in the entire park.
The herded everyone onto the small island-like portion where the restaurant is, and closed the bridge. This lasted about 1-1/2 hours. Although it was still raining, I guess the lightning threat was gone, so they opened the bridge and let everyone into the water.
We did our dolphin swim about 1-1/2 hours later than scheduled. When we inquired, the trainers told us that if they had to, they would continue the dolphin swims past the 5:00 closing time to make sure everyone got their chance.
I would imagine that if they had a very lengthly delay, they would give rainchecks to anyone they could not fit in.