Rhaenys expression grew serious.
"That would mean war," she said with complete sincerity.
As the Greeks say...
Alors, c'est la guerre
If it is the "order of things", it is only because Rhaenys let it be. She had and has a
dragon. At the time of the Great Council, she was one of only two dragonriders in the whole wide world. She and Meleys would only have needed to go against Daemon and Caraxes upon Jaehaerys' death. If she had won that challenge, Viserys' claim would have crumbled to dust. Wherever the lords and lords paramount stand, whatever armies they bring to the field, it doesn't matter if one side has a monopoly on dragons. She could have gone to war against the Council's decision upon Jaehaerys' death. She chose not to. That is the only reason why it is the "order of things".
Which, I think, is an object lesson to us. We should not be afraid to use force to defend our rights, and should not leave them up to the lords of the realm, who are our lesser.
So in that vein...
"The man's behavior was abhorrent for sure," Lord Strong acknowledged, "and your actions did strengthen Lady Jeyne's position well, removing a key figure of opposition without her being marked as a kinslayer, something that would not have been possible otherwise, but you have undermined your position in the process. To the realm at large, you seem easily provoked and emotional."
And otherwise the realm at large would not have taken notice, but still just seen the weak woman in us. If we have to choose, being perceived as prickly but dangerous is still the less bad reputation to have. Ultimately, Aegon didn't win the kingdom by laws, either, but by dragons and force.
And speaking of that...
How is it a threat to let him ride a dragon?
To quote the venerable Septon Barth, the longtime Hand of our great-grandfather Jaehaerys here:
"The power of the Targaryens derives from their dragons, those fearsome beasts who once laid waste to Harrenhal and destroyed two kings upon the Field of Fire. King Jaehaerys knows this, just as his grandsire Aegon did; the power is always there, and with it the threat. His Grace also grasps a truth that Queen Rhaena does not, however; the threat is most effective when left unspoken. The lords of the realm are proud men all, and little is gained by shaming them. A wise king will always let them keep their dignity. Show them a dragon, aye. They will remember. Speak openly of burning down their halls, boast of how you fed their own kin to your dragons, and you will only inflame them and set their hearts against you."
(from Fire and Blood)
Just casually showing how awesome the power of flight alone is, and what advantage it grants you, without uttering any overt threats at all... that would fall squarely into that tradition. And that is how it could, and even likely would be taken. The threat is always there, and the lords will remember. Princes as well.