Jaime remembered Aerys II always becoming sexually aroused after burning someone alive. With Robert's Rebellion in full swing, Aerys was burning people more and more often. Jaime specifically remembered Aerys II visiting Rhaella and then Rhaella leaving the next day for Dragonstone. If I recall correctly, Daenerys was born 9 months after Rhaella left KL for Dragonstone. The assumption we are supposed to make is that Aerys is her father.
Of course, GRRM gives us much information from which we are supposed to draw conclusion.
For example, Eddard claims Jon as his *******, but will not divulge the mother's identity. Eddard quashes the rumor that Ashara Dayne is Jon's mother, but only tells Catelyn that "Jon is my blood." The conclusion at which we all arrived in our first reading is that Eddard is Jon's father... but the really the facts only state that Eddard detests lying.
Is there any information that Rhaella had a lover? If Rhaegar or Aerys II is Jon's real father, then his mother's blood shows clearly in his appearance. Maybe the same could happen with Rhaella... though, it seems the Valyrian blood runs pure in Dany, eg. scalding hot baths, lived through funeral pyre, hatched dragons, rides Drogon.
I don't think there are any real connections to any lovers for Rhaella. But I suppose I could imagine two... Ser Willem Darry was Dany's guardian until he passed away. She had fond memories of him.
The second would be Tywin. Tywin might have known of Aerys' rape of Joanna. He probably suspected it. He may have imagined she willingly betrayed him... that would explain his doubts to Tyrion's paternity. Mayhaps he wanted revenge upon Aerys II by seducing his wife.... The main problem with this (in as far as Dany is concerned) is that Robert's Rebellion was causing havoc in the Seven Kingdoms and we know that Tywin was ensconced in Casterly Rock with all his strength. He would have needed to travel incognito to KL to seduce Rhaella (and mayhaps to instruct Jaime). Anyway, she was long gone by the time Tywin sacked KL.
This type of revenge seems petty. It seems beneath Tywin. His revenge was 1) reclaiming Jaime from Aerys, 2) Aerys' death, 3) the sacking of Aery's capital, 4) the end of the Targaryen dynasty, and 5) replacing Aerys' own granchildren with Tywin's .
And yet, we do know that Tywin took Shae to his bed. Was it petty revenge upon Tyrion to show who was the real man? Could he have done the same to Aerys?
I think Dany is Aerys' daughter.