Recently, an individual created a video posing the question, “What if Anakin killed Obi-Wan.” He then goes on to explain his theories of what might happen.
Anakin would find Padme and she’d probably still die if Darth Sidious couldn’t save her which seems likely. Luke and Leia would be trained in the ways of the dark side from an early age. Now I do disagree with a couple of things: First, assuming Luke and Leia do make it to an age where they can battle to become Vader’s heir, we have to assume that Vader has already overthrown the Emperor. Without Luke and Leia, we know that Vader hasn’t turned on the emperor until Luke’s life is in danger at the end of Return of the Jedi. If Vader did not overthrow the emperor then it is possible the emperor would eventually turn on Vader, possibly with the assistance of Luke or Leia and the Emperor would take one of them as his apprentice instead.
Also, the “Rule of Two” can be a bit confusing for some people. So first, let me explain that the idea comes from three books: [the Darth Bane trilogy]. Basically, for thousands of years the Sith have plotted, schemed and betrayed in their lust for power. This has often weakened the various empires as they are unable to unite for long against the Jedi and the republics. So along comes Darth Bane. All of the other sith are believed killed except for Darth Bane and his apprentice(also a buttload of Jedi at the same time). The rule of two says: “Two there should be; no more, no less. One to embody the power, the other to crave it.” So Bane takes on an apprentice named Zannah and eventually from that point until a thousand years later when Darth Plagueis and Darth Sidious come along, the rule is upheld.
Now here’s the thing, those of you who’ve watched the Star Wars movies and the Clone Wars and Rebels cartoons might be wondering, “Well, how could the Emperor have Count Dooku and Darth Maul at the same time–and how could Count Dooku have Asajj Ventress as his apprentice without killing Sidious?” Simple: they did not respect the Rule of Two. This disregard begins with [Darth Plagueis].
So going back to the video above: Vader could easily allow both children to thrive and even find their own apprentices. However, that would be unnecessary with the Jedi defeated and an empire at his disposal. It is also possible that Vader might even kill his own children and that would not be the first for a sith lord to do.
In Star Wars the Old Republic, we have Emperor Valkorian and he happens to have a son and a daughter. The son does want his father dead and the daughter appears to be content being behind the son. I would not be surprised if it were the same for Luke and Leia with one of the two craving the top spot and the other in support.
Of course, both the Darth Bane trilogy and the Old Republic are no longer considered part of the Star Wars canon thanks to Disney. So as far as any restrictions on sith numbers. We only have Mace Windu’s comments from the prequel trilogy where he says that there’s usually only two sith. But rules are like weak minds–meant to be broken!