Yeah, I think to add on to what you said, mostly twins or brothers never get along. Usually for a very small conflict that isn't that big of a deal. At this point, it became a trope.
I think real!Ciel holds great grudge against our!Ciel because he feels like he was abandoned by him. He was killed and our!Ciel gained power from it. (Both demonic powers and the position of the heir) Not to mention our!Ciel tooo the ring out of the stomach of real!Ciel's corpse. That's pretty fucked up
Our!Ciel took took real!Ciel's life by all means, and because of Undertaker real!Ciel had to watch it all. Seeing his fiancée with his own brother, who took over the family under his name might've hurt like a bitch. Because of all that he wasn't even mourned by his loved ones.
Our! Ciel however sees it as a mean to achieve his goals, instead of the immoral and wicked nature of all his doing.
You summed it up perfectly.
OCiel never really had any means to do what he wanted, all because of RCiel. He was the younger twin; he wasn't going to inherit a single penny of the Phantomhive fortune, earldom, etc, because that's how inheritance worked back then. RCiel, on the other hand, was going to get everything. OCiel was frail and sickly, and that prevented him from a lot of fun life experiences in his childhood. RCiel got to have them, though, right in front of his eyes. OCiel's first and only dream was to be a toy store owner, one that could help entertain sickly children like himself. And RCiel did not like that at all. This delves into conspiracy theory territory, but I'm absolutely positive RCiel had a direct hand in the Phantomhive attack, whether he intended for his and his brother's kidnapping or not, because of OCiel's desire to leave his side. I'm still not totally convinced he's not behind OCiel's initial asthma onset. It'd be some combined form of Munchausen syndrome and narcissism; keeping OCiel physically weak and dependent on him because he grew up with the notion that he has to be the older, stronger, "better" brother.
RCiel has always been a block for OCiel. He was always preferred, always wanted, always "better." OCiel played second fiddle from literally day 1. Now, with RCiel out of the way, and armed with his name, OCiel FINALLY had the means to do what he always wanted. Look at what he did in three years: opened a toy business, made it a successful corporation from his own hard work, did not hesitate to take on the dangerous family Guard Dog business at 10 years old, and taking on the matters concerning the Phantomhive's land and those who lived on it. He did it all. Sure, Sebastian helped to keep him alive and worked as a PA for him, but it's obvious that OCiel masterminded all the business decisions; Sebastian was just an extension of muscle he could flex and contract. And everyone had faith in him from the day he came back, not because he held the title of "Earl" but because he held the title of "Ciel."
Now, RCiel comes back, and no one but his servants gives a single iota of a shit about him anymore. All that work, all those feats he accomplished, all the legwork and strain he pushed himself through to get to where he is, completely out the window. Because he lied. Because he's not "Ciel." And while it's honestly fair in one sense, not trusting someone who steals another's identity, it isn't really fair in another sense, given that the deck was stacked against him from birth.
It's no longer about upholding the name "Ciel" to him; it's about crediting his OWN accomplishments. He did it all, and he was monetarily and emotionally rewarded for it. OCiel had a taste of independence, a taste of being trusted and capable, a taste of what being powerful, feared, intelligent, WANTED was like. And now his dead brother comes out of left field and takes it away. He's second fiddle again. Not only that, but now said brother is pinning HIS disgraces on him. OCiel is taking the fall for him, after he spent all these years giving credit to the name "Ciel".
Anyone would be rightfully and royally pissed.
So yeah. OCiel wants to throw hands. I'm not sure why RCiel wants to fight back though; maybe he's just so confident he'll win again because he's that narcissistic.
To be honest I don’t really understand where this conflict between the twins is coming from... I don’t get it they’ve reunited after all the tragedy in their lives?? And they decide to argue about the position of the heir?? REALLY???
Look I get it. After all the trauma they’ve been through it makes sense why they wouldn’t perfectly get along. I don’t expect them to have no complicated feelings for one another. But this battle for heir seems so stupid to me. Why not instead join sides and find out why the hell their parents were killed???? What happened to revenge???? I feel the author is really desperate for them to not get along but just couldn’t write a good narrative for it.