Bella might be extremely embarrassed. She would probably blush and stutter, trying to come up with an explanation for their situation. Since she loves her father and doesn't want to disappoint him, she'd be very flustered.
They could also react by being protective of each other. Bella might step in front of Edward as if to shield him from Charlie's potential anger, and Edward might put a reassuring hand on Bella's shoulder, showing that they are a united front even in this unexpected situation.
Together, they would likely try to make Renesmee understand that their relationship is special and that her presence is also special. They might give her a hug or some form of affectionate gesture to show that they are a family unit and that her walking in is just a normal part of family life, even if it was an intrusion on their private time.
Carlisle would probably be very calm and composed. He might give Bella a reassuring smile and say something like 'It's all right, Bella.' Esme, on the other hand, might look a bit flustered at first but then quickly regain her composure and act as if nothing out of the ordinary had happened.
Edward would probably be very confused at first. He would try to understand why Bella would leave him for Rosalie. He might start to analyze all their past interactions, looking for signs that he missed. Eventually, he could become angry, not at Bella directly, but at the situation. He might also feel a sense of betrayal, not just from Bella but also from Rosalie in a way, since Rosalie is 'taking' Bella away from him.
Bella would be heartbroken. She has put so much trust in Edward, and this act of cheating would make her question everything. She might become angry and lash out at both Edward and Tanya. She could also become very sad and isolate herself from others.
One possibility is that Charlie is shocked and immediately starts asking a lot of questions. He might be worried about his daughter being alone with Edward. For example, he could demand to know what their relationship really is.
Some fans might be very shocked as it goes against the traditional relationship perception in the original series. They would find it disturbing because of the father - daughter - like relationship they had in the source material.
Edward could use his mind - reading ability. He reads Charlie's intentions and plans his moves accordingly. If Charlie is about to make a decision that Edward believes will be bad for Bella, he can intervene at the right time. He might also be able to manipulate the situation subtly so that Charlie changes his mind without realizing it.
Edward would be completely devastated. He would likely go into a blind rage and seek out whoever was responsible for Bella's death. His love for her was so intense that he would stop at nothing to avenge her.
Some fans would be outraged. Edward and Bella's relationship is iconic, and any deviation from their loyalty to each other would be unacceptable to them.
Some fans might be really disappointed. Edward and Bella's relationship is a central part of the Twilight saga, and seeing Edward ignore Bella goes against the idea of their epic love. They would probably feel sad that the loving Edward they know from the original story is acting this way.