What do you think would happen if the following changes occurred?

[Baelarys the Bastard]

The Changes: Rhaegar marries Cersei, Jaime marries Elia, assuming Rhaegar still crowns Lyanna and R+L=J

Here’s some of my thoughts 

Rhaegar marries Cersei

     - she gives him some legitimate children, some incest children 

     - Tywin remains Hand

Jaime marries Elia

     -if Jaimie doesn’t screw up as bad as Rhaegar did then a strong Lannister-Martell alliance

     -Arianne might be bethrothed to Viserys 

Robert’s Rebellion still occurs

     - Jon is still born

     - Robert dies, Stannis is sent to the wall and Renly is a ward at King’s Landing

     -Jon Arryn could lose the Vale, maybe Jon Conn could earn it? 

              - Lysa might be remarried to him making a Robin Baelish more likely IMO

      - There might be mercy towards the north 

Greyjoy Rebellion still happens 

- Theon could be warded at King’s Landing 

Wot5k

-if Cersei’s first born son just so happens to be an incest child or possibly just a mad targ a war could break out

- I can see Viserys taking on a Renly/Stannis role

- I don’t know if Jon would join in the fighting if he felt it was his duty he might 

- the Greyjoys might pull the same tricks they did in the original timeline 

The North and Winterfell

- I doubt Eddard would be made Hand so no reason for him to go to King’s Landing 

- The north would rally behind Jon 

-Sansa might still be betrothed to the first-born prince so a Sansa hostage is still likely

Thats all I got for now but there’s still some lingering questions 

What would Dany be up to?

Would Littlefinger still find a way to make an impact?

Who would the Tyrells support?

could Faegon be cooking up another Blackfyre campaign across the narrow sea in this timeline?

Who is going to hatch dragon eggs ?

Who is gonna be Azor Ahai?

 

 

[RevolverAxolot]

This would drastically change the story and probably not for the better.

For starters, If Rhaegar and Cersei & Jaime and Elia married, there would be no incest kids as Jaime would be in Casterly Rock while Cersei would be in King’s Landing or on Dragonstone. While they could still get in bed with each other during the occasional visit, it would be few and far between.

 

I assume Rhaegar still kidnaps/runs away with Lyanna, which is what leads to RR. If Robert failed during the Battle On The Trident, Ned would probably be killed so he couldn’t relieve Storms End, which probably would have lead to the death of the inhabitants (even with Davos’s food.) Assuming R+L=J, if Jon is still born and Lyanna presumably dies, Jon would possibly get taken in by Rhaegar, the North (ruled presumably by Benjen) would be unlikely to see him. 

 

If RR failed then the Greyjoy Rebellion would not happen considering they were inspired by the success of Robert’s Rebellion. I also doubt the WoT5K would happen.

 

As for your lingering questions;

Dany’s would eventually just be married off (possibly to Viserys)

Littlefinger would never gain any power as he wouldn’t be appointed to Master of Coin due to the lack of Jon Arryn. 

FAegon would either not happen due to not being fake or would have to actually go by Aegon Blackfyre.

Nobody would hatch the dragon eggs, as they would never be given to Dany.

 

[Sydney Mae]

What you get is a completely different story.  For an example of how too many changes can drastically affect the story you need to look no further than the show.  It's not even the same story anymore.  Same names and same places but that's all. 

[Lord Lannister]

I'm sure you could find an appropriate entry on fanfiction.net

[Baelarys the Bastard]

bump

[LyrnaSnowBunnyAvenger]

I'm really not trying to be nasty or knock you or anything like that, my genuine question is what is the point of threads like this (of which there are many)?  If you want fan fiction, I'm sure there are plenty of websites dedicated to that - I'm not a fan of it, so I wouldn't know but I'm sure Google could answer that. 

What if Bran wasn't thrown out of a window?  What if Hodor was a genius on par with Stephen Hawking? What if Cat got it on with Jon instead of being so incredibly inept and stupid? It would be a different story and one I may not like as much.  Yes, I get that we all get bored waiting (and waiting, waiting, waiting) for the next installment, but "what if...some completely crazy thing so out of line with the story...." just doesn't make sense to me.   

[Morte]

I'm with @LyrnaSnowBunnyAvenger here: Your first premise alone undoes the complete story, as Rhaegars first and foremost reason for the abduction of Lyanna is, that Elia is unable to bear another child, aka the third head of the dragon. As Rhaegar wouldn't have disappointed and hurt Cersei as Robert did, she would have been at least _more_ faithful (maybe even completely) and Rhaegar would at least have got his three children. He isn't Robert, so "love" alone would not be a reason for him to dangle with Lyanna.

So, no: No tower of joy, no child born there, no rebellion, no dragons, etc. No Song of Ice and Fire.

[Lyanna would get a very unhappy marriage with Robert; if Tywin can no longer control Aerys' madness, he, Rhaegar and the Kingsguard would get the king to retire (as was indeed planed by Rhaegar and his friends); Cat would marry Brandon (most likely not as happy as with Ned); well: and maybe Ned, as the second son _could_ indeed get his father to allow him to marry Ashara (if they were indeed in love), so this two would be happy - not really enough story for seven books, eh?]