Personally, Rhaenys would've been an absolutely brilliant ruler. One that would rival that of Jaeharys. It was the wrong decision for Jahaerys to choose Viserys, and I'm going to tell you why!

This is all hypothetical but even so, I'm happy for people to say their piece in the comments. I love talking about HoTD -`♡´-

Let's just say she was heir ever since her father (Aemon) died. With her mother, Jocelyn, grieving I think Alysanne would step in and help with her granddaughter.

Alysanne wasn't called 'The Good Queen' for nothing. She brought a lot of change in Westeros; especially for the women. Therefore, I think her mentorship would guide Rhaenys perfectly. This would lead to Rhaenys making Alysanne the Hand of the Queen until age overcame her.

Rhaenys and Corlys would still marry aswell as having Laenor and Laena. Corlys wouldn't be at sea as much, and Vaemond would have more of a say in Driftmark.

The royals/council members etc wouldn't like the idea of a woman on the throne. But Rhaenys would show them how ruling is actually done.

With every decision she has grace. She isn't hot-headed and would only use Meleys when absolutely necessary.

Dragonstone would be both Laenor and Laena's until it was time to marry.

Alicent and Viserys wouldn't be married - Aemma would still be alive as she wouldn't have been pushed to have so many pregnancies. Or maybe she did die in childbirth, but Viserys told the maesters to do whatever they could to help Aemma.

Viserys would remain unmarried for the rest of his life

Alicent and Rhaenyra are still strong friends ;)

Viserys might not even live in the Red Keep? I'm not sure on that one. Possibly he would and Rhaenyra would grow up around Aemma? And Aemma would automatically adopt Alicent as one of her own children.

OR

Rhaenys does push for Viserys to get married again, and if somehow it's Alicent - then she isn't a young girl but a woman now. And as she has been shown love through Aemma, she respects that woman, even in death. So, Aegon, Helaena, Aemond & Dareon exist (however this would bring challenges to the thrown even more. So the marriage to whom Viserys would take as a second wife would be one of great thought.)

Otto would have a terrible time trying to gain power for himself and his family. However, Rhaenys knows Oldtown is very rich and influential, so maybe Alicent and Laenor marry?

Daemon still has skills that are useful to Rhaenys and the Targaryen Dynasty. But Rhaenys would have always known that Daemon wanted Rhaenyra... maybe she didn't involve herself, or MAYBE she wed Rhaenyra & Harwin...

𝐒𝐨, 𝐖𝐨𝐮𝐥𝐝 𝐓𝐡𝐞 𝐃𝐚𝐧𝐜𝐞 𝐎𝐟 𝐓𝐡𝐞 𝐃𝐫𝐚𝐠𝐨𝐧𝐬 𝐒𝐭𝐢𝐥𝐥 𝐎𝐜𝐜𝐮𝐫𝐫𝐞𝐝?

Firstly, who thinks the Iron Throne should be there's?

Viserys is the next 'best' claim to the Throne. However, Rhaenys has more children and therefore more heirs. I think Viserys would rather not be the King as well.

Daemon; who made himself think that the seat would be best for him. But over time, with Rhaenys' guidance - his hunger would be used in a different way. She would show Daemon that the Crown and the Throne doesn't make you a god. You have responsibilities beyong comprehension.