I love the series, but it drives me nuts that Rhaenyra and Daemon don't have representation on the small council. They seemingly don't collect any information on the happenings in King's Landing even though they fully understand that the Green's are plotting to take the throne.
I think that is somewhat yet to be seen. I think Rhaenyra believes that once the King dies, that she will ascend to the throne as was planned and expected by all the kingdom. But with Alicent being in the kings chamber and misinterpreting the song of ice and fire, that moved things in a direction that Rhaenyra and company didn't expect. Additionally, they probably felt like they put Alicent and company in place after the Kings ruling on Driftmark in the previous episode before they left after dinner.
If they had stayed in Kings landing, I think things would have been different. But when they get the news that the King died AND Aegon was crowned king, that is what will probably set them off. I think up to this point, Rhaenyra and company have been playing typical court politics while Alicent and company have been playing to stage a coup (as we saw in the small council, Otto and a couple others had been gathering allies for such an event).