1. Had King Robert Baratheon and Cersei had had a true born son, Joffrey would not have been made the King after Robert’s death.
Plus Robert’s heir would have married Sansa and she would not have been betrothed to Joffrey. He might have Cersei’s cunningness but not her cruelty, hence this would result a lot more in Ned Stark’s death. Ned being alive changes many events. Arya would not have run away nor would Sansa have been married to Tyrion and Ramsay. Robb would have been alive and the Red wedding would not have happened.
Catelyn would not abduct Tyrion and he would not meet Bronn. Neither would Jaime make a duel with Ned and wound him in the process. Hence, Robb would not have captured Jaime and Jaime’s hand would still have his dueling hand. Brienne would have been under the service of Renly Baratheon. Maybe Robert would have been alive as his true born son would have loved him. And for Cersei her children are important to her. Now, Stannis would not have any motive in killing Renly as Robert would still be alive. Melisandre would have encouraged Stannis to kill Robert the way he killed Renly so as to take the Iron Throne.
As Robert dies being killed by Stannis, his son wages a war against Stannis in order to avenge his father’s death. Stannis loses his fleet and a majority of his army in the war that ensues. Stannis makes a hasty retreat after the war. Probably he plans to lay low for a while.
2. According to the series, Cersei was once conceived with Robert’s child which she killed in her womb itself with Jaime’s help. Even if she had conceived Robert’s child she would have killed it again. Cersei said that her children are everything to her, but they were Jaime’s children and that was why she loved them. It just shows how much selfish Cersei is.
But assuming Cersei lets a child of Robert live in her womb and it eventually sees the world. If there is one thing about Cersei, she loves all her children fiercely and that would have been the same thing with Robert’s child, as all of Jaime’s children also had the same Baratheon name title. Cersei would have wanted the same things for all her children and would have treated them fairly. Maybe Robert’s child would have been like Robert, a great warrior and a capable general; hence, his child would have been compassionate, strong and ambitious but certainly not evil like Cersei.
Suppose this child is named the King of the Iron throne and protector of the Seven Kingdoms, then he would have been a capable ruler and a strategist in terms of warfare. He would not have made any of the mistakes Robb made during his rebellion and would not have been naïve like the Starks. Even with Cersei being the queen mother and Tywin Lannister, becoming the hand of the king, certain events that shook the honor of the Starks such as imprisoning and beheading Ned and dishonoring Sansa would have been avoided.
3. Had a child been born to Robert and Cersei been a girl, it would have been married over to Robb Stark. Hence, this would have totally prevented the Red wedding incident as Robb would not have been promised over to one of the Frey girls and the Lannisters would not like their own daughter to become a widow.
Had the girl existed then the war of the five kings wouldn’t happen. The Starks, Renly, Iron Island and Stannis would not rebel against the Iron throne as the legitimate heir exists and her husband can become king after Robert.
Cersei loved all her children and had she let Robert’s child survive in her womb things would have been a lot much different for the Lannisters, Baratheons and Starks alike. Many of the battles fought in the series could have been avoided and all of Cersei’s children would have lived. This would mean that she would not become the Queen of the Seven Kingdoms, but she would have been left with her children. That would have been a consolation.