Does anyone in Westeros know that Daenerys is the mother to three dragons in Mereen aside from the small council? Such as Bran, Tommen, Doran, Ramsay etc? Also are there still many loyal to the Targaryen family who would support Dany if she was to try conquer the Iron Throne?
By the end of A Dance With Dragons, there are a handful of people in Westeros who know about Dany and her dragons. Assume the rest of this answer will have spoilers.
First and foremost is Doran Martell, who sends his son to Essos to bring back Dany and/or her dragons and ally them to Dorne. Those also in the know include his close confident Aero Hotah and Arianne Martell.
Euron Greyjoy tells the Ironborn that there are three dragons still alive in the world at the Kingsmoot. So basically every Iron Islander of note knows about the dragons, but I'm not sure that he tells them that its the Targeryon heir who owns them. The entire Iron Fleet presumably knows once they depart for Meereen, but at that point they're no longer in Westeros.
Archmaester Marwyn learns about the dragons using magical means. But again, he immediately leaves for Meereen as soon as we meet him. But he tells Alleras and Pate (probably actually Jaqen H'ghar) before he goes.
Samwell Tarly and Gilly both learn about Dany and her dragons from the sailors on The Cinnamon Wind, who saw the dragons when they were in Qarth. Aemon Targeryon learns about them before he died en route to the Citadel.
You mention the Small Council, but most of them always dismissed the stories of Dany's dragons as fables. Varys presumably knows the truth, since Jorah was in his employ until Qarth and his good friend Ilyrio knows. Tywin Lannister gave some indication that he believed the tales, but pointed out how the last of the Targeryon dragons all died in their infancy.
You also have to count the countless number of sailors bringing back stories of the dragons from their trips to Essos. This is how Davos Seaworth learns about Dany and the dragons in White Harbor, but we never gets an indication of whether he believes the tales or not.
We are talking about a kind-of-medieval fantasy world:
- There are regular trade links between Meereen and Westeros. The traders transport rumors of dragons in addition to their cargo.
- The rumors are distorted during transmission. Listeners might reject the truth as obvious exaggeration or believe exaggerations as the truth.
- The court in King's Landing has some sort of foreign intelligence collection, but they are limited by their lack of bureaucracy. Agents pass messages to Councillors, who may or may not a hearing in the Small Council. Again, they may or may not be believed.
- There are commercial networks like the Iron Bank of Braavos.
Then there are the more fantasy-like parts of the setting:
- The Maesters have their raven mail.
- The Red Priests look into flames.
Summarized, important people have heard about the dragons. They might believe it or not, or they might not care.