Jaime's trial by combat in chapter 120 has him lose heavily as Robert smashes every weapon he carries, along with his armor and shield. As one reader puts it, it's also a representation of how his mistakes have caught up with him.
First, he loses his sword - it shows how he's not worthy of being a knight in his own right.
The second sword, his replacement sword, confirms it.
The third sword he picks is Lancel's, who represents his family. Its destruction marks how he cannot hide behind the family name to escape the consequences of his actions anymore, as well as the fact that, on the Wall, his name will mean nothing.
The fourth and fifth sword belong to two redcloaks - the projection of the power and prestige of his family, or, more exactly, his father Tywin's power and prestige. This shows how not even that can save him from the righteous fury that possesses Robert.
Finally, he is stripped of his shield, armor and helmet - a final demonstration of him losing the symbol of the knight he could have been, but chose not to be.
After Dacey Surestone arrives in Winterfell, Robb mentions that they received no word from her in the original timeline. Looking at what was planned for her, she was either forced into prostitution or died on the road. It was only due to the changed circumstances that Tyrion was there in the new timeline.
We know that Joanna Lanister separated the twins because she was worried about just how close they are. We also know the Cersi has always been disturbingly obsessed with what she wants, when she was a girl she murdered her friend for hearing her prophecy, and that after her mother's death she was allowed to be closer to Jaime again. Given this were there other factors than just Tyrion's birth that were responsible for Joanna's death?
Possible, but unlikely. Remember, the biggest reason Cersei hates Tyrion is because, like Tywin, she holds him responsible for Joanna's death.