On the subject of spares: sitting in a spare room is exactly where they belong. If she carried around a bunch of spares, then a generation or two after the ship gets underway, there's parts sitting in drawers, under mattresses, in undocumented parches and more. Inventory control would be vital in such a resource limited scenario, there's no Frys you can just buy another from.
On Cordelia, it sounds as if her AI designer made the classic n00b error of integrating code and data. Her objective records should have been stored in a separate location, whether a database, collection of files, or whatnot. Unless she exists to be an exclusively perceptual intelligence who reports on the history of the family through the veil of personal experience, the data and code don't belong to each other. Clearly, the family didn't perform a good code review!
Now if that's the case, then her role makes more sense. She's an AI, not a portable camera. I imagine her role would be to provide a sense of continuity for the family, an unbroken connection to the fam as they were when they left spacedock. Without that, the group that arrives might be alien in motivations and values compared to the one that invested everything in colonization.
Finally, I respectfully disagree with the implicit assertion that the family was heartless. In an environment like they have, generosity with resources isn't possible without screwing your descendants. Letting the uncle live without pulling his weight might be an impossibility in their situation, depending on how their resources are implemented. What happens if medical care becomes impossible late in the flight because two generations of senior citizens consumed all of the medical supplies early in the trip? They may not have the option of making exceptions if it may hurt their children or descendants, they basically hold the resources of the ship in trust.
Same with allowing emotionally unstable people to reproduce. We have safety valves in Earth that allow us to ignore or even benefit from outriders who may even contribute to our genetic richness over time even with short term problems, but the rules change in a confined environment. If her brother produced kids with magnified emotional instability traits (limited gene pool, eventually you're gonna cross the streams) and two or three generations later the ship has a mutiny or massive social breakdown, everyone could die.
It sucks, but the reality if shipboard life would necessarily be different from what we experience on mother dirt here.