Perhaps there's an external threat that causes a rift between them. For example, a new vampire coven arrives. Bella wants to handle it one way, believing it's for Renesmee's protection, but Renesmee has her own ideas on how to deal with it. Their different approaches lead to an intense fight.
It could be about a misunderstanding. Renesmee might think Bella is being overprotective in a wrong way, like not allowing her to have normal relationships with others. This misunderstanding can escalate into a fight as Renesmee rebels against Bella's restrictions.
Bella might be more likely to win. She has more experience as a vampire and has been through many tough situations. Her combat skills and knowledge of the vampire world could give her an edge over Renesmee.
Perhaps the Cullen family has to deal with the shockwaves of Bella's death. They may face challenges from the vampire community as Renesmee is a unique being. Some vampires might see her as a threat or an abomination. The family would then have to protect Renesmee at all costs while also mourning Bella.
One possible reason could be Renesmee's growing independence. As she matures, she might want to make her own decisions which could conflict with Edward's over - protective nature. For example, she may want to explore the world more freely, while Edward, fearing for her safety, tries to restrict her.
In the fanfiction, it could be that they fight due to differences in their beliefs or values. Bella, with her human - turned - vampire mindset, might have different ideas about how to deal with certain supernatural situations compared to Paul, a werewolf. Their clashing views could result in a physical or verbal fight as they both try to impose their own ways of handling things.
The fanfiction could revolve around Renesmee's discovery of her pregnancy. She might initially be in shock or disbelief. Then, as the story progresses, it could detail how she starts to make plans for the future. There could be a lot of internal monologue about her hopes and fears for the child, and how she wants to raise it differently from how she was raised, given her unique situation.
One possible plot could be that there is a powerful new item in their world. Sonic thinks it should be used immediately to stop Dr. Eggman, but Tails believes they need to study it more first. This disagreement leads to a fight as Sonic tries to take the item by force and Tails tries to stop him.
A plot could involve Renesmee's love life. Since she is a special being, finding a suitable partner would be difficult. It could be a story of her falling in love with a human who is initially afraid of her but gradually comes to accept her. Edward and Bella would be there to guide her through this new experience, while also being protective. Or perhaps a plot where Renesmee discovers a hidden power within herself that has been passed down from an ancient vampire ancestor, and she has to learn to control it with the help of Edward and Bella.
Maybe a plot where Renesmee has to face some sort of vampire - human conflict that her parents once faced, but in a different context. Since she is part - vampire and part - human, she could be a bridge between the two worlds and strive to bring peace. She could use her understanding of both sides to defuse tense situations.
One possibility is that Renesmee is simply curious. She might ask them what they are doing in a very innocent way. For example, if they are having a private moment, she could break the mood but also add a touch of humor to the situation as they quickly adjust to her presence.
Well, it could be about Bella having a secret power that she has to hide from the world in the fanfiction. Maybe she can communicate with animals secretly and is afraid of being seen as a freak.