My last house had all sorts of awful water issues like this, so I feel your pain...
In a flash-flood type situation, there isn't much that you're going to do with a pump. You didn't describe the terrain too much, but you need to find a way to redirect some of the water in a different direction. If you have gutters that empty in the area, direct the water further away from the house.
Other things that may help:
- Remove paved or other water-impervious areas.
- Plant vegetation that will absorb water flow. Google "rain garden"
- Build a French drain around the area.
- If it makes sense, dig a drywell.
When municipal systems have issues with flash-flood rain, they install cisterns to capture some of the overflow if redirection can't work.