Well… you seem to have missed the point. The Rule of Two is all about there can only be two Sith because they are always trying to kill each other.
I’m aware of the Rule of Two but it is by no means a theme firmly established in the movies. There’s scope to believe whatever you want about the Sith in the George Lucas saga. I don’t think it’s any great “rule”, maybe it is, but I see it as Palpatine’s lust for the power of the force.
For Palpatine it really becomes the rule of three because he has an apprentice, but he always has backups floating around in case his apprentice gets too powerful and might kill him.
I think he uses other people, we see this in Attack of the Clones where he uses and betrays Count Dooku. There’s scope to believe what you want - perhaps its self-preservation because it’s the Sith way for the apprentice to kill his master. In fact Dooku has already betrayed Palpatine at this point, because he ratted him out to Obi-Wan when he tells him “the Republic is now under the control of a Dark Lord of the Sith … hundreds of senators are under the influence of a Sith Lord called Darth Sidious.” He couldn’t have been more specific than that, but Obi-Wan didn’t believe him. On the other hand is that Palpatine has no loyalty whatsoever to Dooku and is interested in replacing him with Anakin - perhaps Dooku has sensed this and is acting out of his own self-interest/preservation. There’s no one opinion on this that is necessarily proven right, as with good storytelling there’s scope for a range of possibilities.
His goal in ROTJ was for Luke to replace Vader. But Vader is plotting the same thing.
Palpatine’s goal is to rule the galaxy as supreme Emperor. Everything else is second to that really. That’s part of his character arc in the prequels - he creates wars by influencing both sides into war (even going so far as to arming both sides so that they can go to war) so that he can get the power to overthrow the Republic and create his own Galactic Empire. He’s motivated by power. Some of the execution of this in the prequels is very clumsy - like when Jar Jar sits in for Padme as a Senator and sponsors his bid for “emergency powers” (it does make sense in that he chases her away with assassins from being able to block him, but what doesn’t make any sense is Jar Jar doing her job, however it could have been done a lot better and certainly without Jar Jar).
One of the reasons he uses Anakin is because he wants to use him to manipulate the Jedi Council - that doesn’t work out exactly as he had planned, but he’s still able to get Anakin to betray the Jedi.
He is either a genius have having multiple options or a genius at finding out how to turn a bad situation to his advantage.
I don’t see it that way that he has “multiple options”, I think he uses “multiple strategies” to achieve his primary goal. So he secretly commissions an army to be built for the Republic. He convinces the Trade Federation to start a war with Naboo. He makes friends with the power-brokers in the Republic’s Senate so he can manipulate votes (a power broker is a politician who controls a large block of votes). He white-ants the incumbent Chancellor by manipulating the very young and impressionable Queen Padme Amidala. I believe this is when he decides to destroy the Sith, so that they will not be able to oppose him, and so that he can pursue his main goal to ultimately become the Supreme Galactic Emperor. So he sends his Sith apprentice to his death. 10 years later Padme doesn’t trust him, obviously, she probably recognises she was manipulated. She blocks his bid for an army, so he chases her away with assassins so he can create an army, create a full-scale war, put the Republic into a catastrophic emergency that justifies granting him “emergency powers”. Once he’s in this position, as Supreme Chancellor of the Republic, he unleashes the clone army he had secretly made which is much stronger than the Trade Federation and their allies, thereby guaranteeing him success in the war (this will make him a war hero to the Republic). This enables him to build more arms for the Republic. Once he has power, and he’s all but won the galactic war, the only ones that can oppose him are the Jedi, so he destroys them. He dismantles the Republic so he can create his ideal Galactic Empire and rule as Emperor, and from there he continues building their arms.
The whole story and character-act is completely coherent and consistent, at least as far as Palpatine is concerned. Dooku gets himself caught up in his plot somehow, and that’s actually quite a good curve-ball to his story (he can’t just rise to power completely unopposed). Where it gets messy is with some of the other characters like Jar Jar and Anakin who behave in ways that achieve Palpatine’s but are not consistent with their own characters.