Behind the scenes
The location of the river is not specified. Robb's army fights there after the Battle of Oxcross and before the Surrender of the Crag. It is therefore likely to be in the northern part of the Westerlands between these two locations. Lannister scouts report that Robb's army remains north of Ashemark shortly after the battle takes place so it is likely in the northern part of the region. The three forks of the Trident are similarly named but only the Red Fork lies near the Westerlands.
In the books
In the A Song of Ice and Fire novels, there is no river named Yellow Fork.