If Anakin Skywalker (Darth Vader) Survived In ROTJ

Another version (not mine)

Here's a different way of how this could've played out. I saw this in the comment section of the Youtube video, and I think it was pretty good. (I'm simply copy-and-pasting this, I did not come up with this idea.) Hopefully the original poster, Jessie Hogue, doesn't mind me doing this. 

Jessie Hogue: I really like almost all of your other theories, but honestly and with all due respect, I don't agree with this one. I think the Rebellion knows enough about the Force from history and from Luke, Obi-Wan and possibly a couple more of their allies, to know that sometimes, Darksiders come back to the light and are entirely different people. 

Also, if Luke tells them 'He's not a threat anymore, he's turned from the Dark Side, he's good now', I think they would give him the benefit of the doubt right from the start, especially Mon Mothma and other important figures, because Luke's accomplishments are the only reason the Rebellion was not entirely destroyed time and again. If it wasn't for him, they would all be dead already and they know it: they owe it to him to at least give him the chance to prove that Vader is reformed as he claims. Considering his importance and rank in the Rebellion, and the fact that he made it clear that he went on the second Death Star to try to save his father because he knew there was still good in him, I think it is very unlikely that Mon Mothma and the others didn't know of his intentions, and also unlikely that they would have tried to stop him, if only because if anybody knows this, it'd be him. 

I believe they would support him, and they would ease the concerns of others towards the former Sith Lord rather than let them decide his fate. I believe they would have provided immediate, and willing, medical care to him (while keeping a healthy number of armed, yet trusted, elite guards to watch him just in case), and supervised his 'welcome' in the Alliance/New Republic with little more than a 'I hope you're right about this, Luke', because if it wasn't for him, they would never have made it to that point. Given the chance, Vader would have proven he was definitely back from the Dark, and would have become a formidable ally to the Republic and the future New Jedi Order. 

Again, I did not come up with this idea. Also, not to be rude, but I would still say the original video's plot-line was better (of course, this is just a personal opinion); however, Jessie Hogue's idea was really good, too.