I don't actually think Cesare rode back in the carriage with Lucrezia, judging by his position in the scene where they're back in Rome but go along with it for the sake of Alfonso-angst. I'm a big fan of outsiders' perspectives on pairings and there's an endless wealth of things to explore where Alfonso and C/L are concerned. This also assumes the carriage had an open back, which I also don't think it did.
Alfonso didn't know whether they thought they were gaining some semblance of privacy by riding in the back of the carriage together, but he could still see them as he rode behind. Perhaps because, perversely, he could not look away. He could see their silhouettes in the back of the carriage— touching each other, always touching. Her nestled into his side, running fingers through his hair in the darkness. And cruelly, anything he couldn't see due to the low light was illustrated in vivid and unforgiving detail in his mind's eye. He could see them kissing like frenzied, rabid lovers, with no propriety or regard for her child and the maid sitting there with them. If they were willing to disregard all illusion of being ordinary siblings to kiss and embrace in the mist, what was to stop them now?
In the end, what was one more sin to the Borgias?
Maybe this was the philosophy they subscribed to when they first debased each other. His lip curled of its own volition at the thought. Despite what those in the Vatican might think, he had not been naïve when he married into the Borgia family. He knew of the rumours; the simony that brought Pope Alexander to power, the whispered accusations of fratricide tainting Cesare Borgia's already muddied name, he had heard it all. Despite everything, he loved Lucrezia and had once thought she might feel the same way too, or at least grow to. That conviction of her reciprocating his love had slipped away over time, like water through his fingers— and now, watching their shadows clutch at one another in way that defined the very word 'sin', he couldn't understand how he could have ever been so obtuse as to believe his wife loved him, or even felt anything real for him. All her devotion was reserved for one person only.
Once back in Rome, he hurries to meet her and help down from the carriage and feels Cesare's eyes burn into him. He feels a strange, sudden need to get her away from Cesare, as though it would save her from their transgressions, as though it wasn't long since too late. He hurries her inside anyway, gripping her arm only a little too tightly, but she twists away from him easily to take Giovanni from the maid and waits for Cesare anyway. Alfonso clenches his teeth and walks ahead to their room. Cesare follows them there, of course. Always the dark shadow over what could have been happiness for both himself and Lucrezia.
Cesare and Lucrezia talk quietly by Giovanni's crib, and he looks over at Alfonso, saying something about him that makes Lucrezia smile before he finally leaves. Alfonso cannot help but bring it up and Lucrezia lies to him so smoothly that if the scales had not fallen from his eyes over the course of this long night, he might have believed her when she told him he was the light of her days. Somebody else filled that role and it was too late to pretend otherwise and this is what he tells her. All pretence of a happy marriage between them falls from her face then. It hurts more than it should, given the events of the evening. Part of him wanted to still be lied to, wanted her to insist that he was her only love, that the bond between her and her brother was familial and not based on the most ungodly of desires. She offers no such denials or even excuses as she reminds him marriage means a lifetime being bound to each other.
He can see the Borgia in her now, clearer than he ever did before—fiercely insular, expedient to the point of being ruthless with others as was needed, discarding those who became useless. He sees it now; she is the very mirror image of her brother. The infamous, monstrous Borgia blood raged in them both.
Cesare warns him against provoking him with a sword pointed at his chest. Once upon a time, when he found Cesare frightening and was meek around him in order to curry his elusive favour, he would have heeded that warning and stopped. He doesn't any more. What else can Cesare Borgia take from him now? Only his life, and as much as it appears Cesare would like to as they 'spar'— he says it himself, he would not for Lucrezia's sake. Alfonso thinks it is a sombre state of affairs when the only matter stopping his own brother (in-law as Cesare coolly reminded him) from killing him is the good opinion -and most likely, warm bed- of his sister.
And just like his sister, Cesare barely offers any denial to the charge laid against him. Only a few weak, vague deflections of rumour as metal clangs together. Alfonso is beginning to learn that this Borgia family really does have no natural shame, let alone apology for their unholy desires and afflictions. It is a lesson learnt the hardest way and learnt much too late. Cesare easily blocks all of Alfonso's offensives, barely breaking a sweat as Alfonso's sword clatters to the ground. Cesare stalks towards him like the apex predator, only to offer back his sword seemingly as a gesture of goodwill.
The look in Cesare's eyes lets him know it is more a stay of execution.