I think rolling opposed CHA checks runs the risk of not being that engaging. Many systems that have engaging social conflict resolution mechanics find ways to make it more engaging - a bit like many RPGs combat systems.
I'm saying this from three perspectives: (i) "top down" theory; (ii) my own actual play experience; and (iii) the fact that I think my Prince Valian experience is probably fairly typical for that system - given the contents of the published material - whereas I don't think I've ever seen D&D actual play reports about jousts, romantic rivalry, founding military orders, etc.
When D&D routinely produces the outcomes
@Reynard is a bit bothered by, whereas other systems routinely produce the outcomes that he is looking for, it's probably worth looking at what those other systems offer that D&D doesn't.
One of those things is to present a game with a specified play focus.
D&D doesnt do that, which is why D&D has a thousand and one 3pp products that do.
Now, I have had all those things happen in my games, and in games I’ve been a player in, without any added rules. OP doesn’t need to learn a new system, they just need to focus on what the sort of game they want, and houserule to taste
if they want to.
How different is an opposed fellowship roll to an opposed Charisma roll? Is it modified by past interactions and some sort of score that represent the relationships involved? There are DMG rules that can be used to do the same thing, or it can be kept even easier and just create a downtime activity for the joust that includes a roll to gain the favor of the crowd, a new paramour, or gain the sponsorship of an existing paramour. The two knights would compete in that one roll, and then go about the joust. The sponsorship would literally be one success or failure in a series of tests to see how well they do in the joust.
That isn’t even new rules, that is just making a new downtime activity, which is about as much “homebrew” as making a unique background.
But knights founding a chivalric order? That is...classic D&D? I mean, I can’t imagine that not happening in a game with the same themes as Prince Valiant.
“You’re all chivalric knights in a world inspired by late medieval French romanticisation of chivalric knights and the kingdoms they fought and died on behalf of. You’re assumed to be good, honorable, and genuine, and things like reputation, (ideally, I know my Arthurian myth too well to expect actually) chaste romance, and defending the weak against the dishonorable strong, are all things that actually matter to any PC in this campaign.”
That’s a perfectly reasonable campaign brief in D&D. Absolutely no rule in 5e D&D actually pushes you toward dungeons, or worrying about treasure, or being homeless. For goodness sakes, your background can be Noble, or Knight, right in the PHB.