Steps for canceling a kiddushin

Hello. I'm not sure I understood the question. When a rabbi testifies against a witness, this is the issue of Sanhedrin 23:2b. "He comes first and then another to dismiss them." There it is proven that a rabbi who testifies about a witness is a rabbi (and not a rabbi), and when he testifies about the parents of the witness (for example, that they are slaves), the conditions were divided as to whether it is kosher or not. According to the halakhic tradition, the sages do not. See Rashi where it is only when testifying about witnesses and not about judges. But in Shulchan If so, the husband and wife are probably the ones who are involved in the matter and not in the case. But I didn't understand what you wrote, "It is their right to be part of the process, but not their obligation." What is this? It seems to me that the public is never considered to be involved in a matter, otherwise judges would not be able to try criminals or decide on personal status laws. People from the public are involved in a matter (see 2:33b on the sabbath that was stolen from the city and more).