Pretty sure the heroine told the first prince a bunch of lies which the first prince believed. Maybe even set up some scenes that could easily be misinterpreted as her having an affair. Remember, MC doesn't behave like what the villainess would and is instead an outgoing girl that actually engaged the heroine in friendship(or at least tried to). My prediction is that the heroine set MC up to which the first prince 100% believed and later makes the lies seem real to the 4th prince as well. When it comes time for confrontation Len declares he accepts her faults and all to which she asks him what the hell does he mean and finally states her piece that no, she had her first kiss stolen by mister 4th prince so she couldn't have had her first time taken already. Heroine's lies are broken (alongside her other sins), first prince despairs, MC happily marries Len and gets her happy end. At least that how I see it. Bonus points if the heroine is also a reincarnator and used her game knowledge to ensnare the prince.
Some other tropes from other works of this genre is that the first prince really didn't want to let the MC go and has much regret, and when the lies are finally broken he despairs because he lost everything and for not believing in the MC (my favorite kind). Another one is that the 1st prince stubbornly defends the heroine even after ample evidence is presented and is stripped of his title and status by the king. Third is that nothing happens to him. He and MC come to an agreement and he wishes her happiness as they mutually part ways.
That's my 2 cents anyways.