You could dig a "dry well" at the low spot as a simple fix- it would require digging a large hole, lining it with water pregnant fabric, and filling with river rock. This will eliminate pooling as it gives water time to permeate into the soil. I did this and it completely stopped my pooling. The size of your hole should be enough to collect any excess water for reference mine was about 10 wheelchair full. As for your trench, others have good suggestions