That revelation of yours is from Swanwick's "The Dragon Line" (1988), first published in Terry's Universe and again in IASFM June 1989.
Merlin is describing how his son became Arthur:
... We agreed he should be raised by Ector, a minor knight and very distant relation. Letters passed back and forth. Oaths were sworn. And on a night, the babe was wrapped in cloth of gold and taken by two lords and two ladies outside of the castle, where I waited disguised as a beggar. I accepted the child, turned, and walked into the woods.
"And once out of sight of the castle, I strangled the brat."
I cried aloud in horror.
"I buried him in the loam, and that was the end of Uther's line. Some way farther in was a woodcutter's hut, and there were horses waiting there, and the wetnurse I had hired for my own child."
"What was the kid's name?" Shikra asked.
"I called him Arthur," Merlin said. "It seemed expedient. I took him to a priest who baptized him, and thence to Sir Ector, whose wife suckled him. And in time my son became king...
The rest of the plot is close to your memory, though the viewpoint character is Mordred himself. The girl, as you say, is his daughter. Merlin tries to trick them into a ritual that would eternally bind Mordred to his will, but Shikra is too fast and stops him. In the end they drive off together, with Merlin trying to charm Shikra.