just my own theories

woah wait im getting some odd vibes on this. really confusing but here's a theory or two:
1) the mom is the princess from the story which would explain why the book archie gives her seems familiar. she "created" the one hit story and story continuation in cordelia's world inspired by the true story in that world but also brought her "son" when she changed worlds. she actually does die and liam poses as her rep to guide her daughter

2) liam is actually archie and archie is liam. the archie from the letters is in the past and the box is like a time portal of some sort, like being able to telephone somebody in the 1950s while you're in the 2000s. liam is also archie BUT archie a lot later in the timeline where he would come across somebody or something that allow him to come to cordelia's world where he would execute the happenings of the letter exchange with the magical box he had before aka its actually one in the same box but traveling through dimensions and time causes it to have another "end" being cordelia's box.

3) similar to the first one, the mother is the princess from the story and created the one hit story but not the story continuation. she makes a deal with some sorcery icon to move to the modern world with her family but there is a price the parents must pay for a happy life for their "son". her husbands dies as a result and she would become sick and die as well. liam would come across the same sorcery icon for a different goal and the deal would relate to either continuing writing that story after the mom had left and try to change the plot or become close to cordelia in both cases would need the box she and archie currently has

tbh none of these theories make sense to me strictly but just random thoughts that would some how, in some way, possibly make sense. the one that makes most sense to me is 2 but that doesn't really describe her mom's background. they also hypothetically do not know how each other look so its very likely that they are related in the past some how