We might argue that since Kenneth has not yet traveled to the past to save Belinda, we cannot know whether Darius goes with him. On that reasoning, though, we cannot know whether Kenneth himself makes the trip or saves Belinda, but the argument is that he does because she is alive. If Darius' mother is not also still alive, then either she did not go with him or they did not save her. However, from the moment Kenneth completes his first mission there is no version of events (following the causal chain) in which Darius does not go with Kenneth.
Perhaps, then, Kenneth already succeeded in saving Belinda, but did not know it. He would have to have done so by whatever he did on that first trip, which seems improbable if anything we concluded about that trip is true, and the more so if saving Belinda is still his mission objective this time. He might not remember that what he did changed the past such that Belinda is alive, but at least he should have recognized that his trip to that time must have altered events in a way that might have caused that change. That he does not imagine that possibility--it is clearly in his mind that he has not yet done anything that could save her, but must do so yet in his own future--tells us that this is not what happened.
Perhaps they did, or will, save Darius' mother, but just as Kenneth is somehow shielded from knowing that Belinda is alive, so too Darius is shielded from knowing that her mother is. How does that work, then? Darius evidently is not shielded against knowing that Belinda is alive, even though she must have been involved in saving her. Perhaps it is simply that they do not know if they have no contact, and Kenneth (having always been involved in the accident) never again saw Belinda. Yet it seems that Darius' father is equally unaware that her mother is still alive, and just as obviously had her mother lived Darius would have seen her probably every day for years thereafter. But is it that her mother never died, but after talking to that ungrateful fourteen-year-old daughter decided she had better things to do with her life and simply never came home again, vanishing without a trace? It is very difficult to imagine how her mother could still be alive and Darius not know this.
Perhaps, we are given to think, Kenneth is delusional. There is no time travel, and the death of Belinda is entirely in his head, invented as a way of protecting himself from the fact that she was never his girlfriend. They don't save Darius' mother because they did not save Belinda either. That is the conclusion we reach if we believe that Kenneth has not created a time machine. What, though, if he has?
We are left with the possibility that having determined to save both Belinda and Darius' mother, our intrepid duo succeeded in the first but not the second. It would be a disappointment, and it is difficult to determine how they might be able to change history so dramatically in the first instance and not adequately in the second. That makes this outcome also unlikely, but not impossible.
It also avoids the problem of an infinity loop, because if Darius is unable to change the past intentionally, she does not undo her own wish to do so, thus creating an N-jump. However it happened, that is the best outcome.