She keeps changing her story because that is what she does. Some people are like that. They don't have a good grasp of the importance of facts and their perception of fact changes from day to day depending on their mood and what else is going on in their life.
I think BD has a good grasp of reality and the importance of facts. Emotions/moods do not change facts. Only when one is trying to circumvent the truth does a story change.
The earrings were part of the description initially given of the items she was believed to have with her. Since she spent time at both parents houses, and since they lived close together, LE would have checked to see if any of those clothing items were at the other house. There is no way that any competent LE officer would fail to do that. And even if they did fail to do that, the description would have been available to CD's side, so surely it would have occurred to them to tell LE that the description was not correct. They didn't.
BD thought Hailey had the earrings on she also told LE she was wearing tennis shoes but those were later found in BD's house, so BD had to change the description to flip flops. BD was running this show, so to speak. I don't think at that point and time CD was allowed by BD to have much say so about anything. LE did look for the items, that is how the tennis shoes were found.
For whatever reason best known to CD's household, that information was not shared with LE.
I mean, it is not like these were random nondescript items. HD had just recieved them and anything that happened to them would have been a big deal. How could someone just forget about that?
At that time I can see where it was just a pair of earrings that were hurting her ears. She took them out. No big deal. I doubt that BD would have listened to anything CD or his girlfriend had to say or offer when it came to giving a description of what she was or wasn't wearing, after all, SD was the last person to see Hailey.
Like I said, maybe they are just really confused people, but it is a problem because it implies that they are not being upfront about everything.