Case assignment is a big problem for formal frameworks that postulate some sort of deep agentive case-like structures like theta roles in GB because whenever the morphology clashes with the deep structure. It's not too difficult to deal with it as part of the morphology module but cases like this have to be dealt with as an exception.
On the other hand, it ...
Correct me if I'm wrong, but it seems pretty straightforward:
From the Halliday's functional standpoint, both sentences are equivalent, since they deliver the same message and have exactly the same communicative implications — in this particular case, they both denote two acting subjects: my mother and I.
From the Chomsky's generativist standpoint, the ...
“‘Me and her’ meets ‘he and I’:
Case, person, and linear ordering in English coordinated pronouns”,
by Thomas Grano (2006) seems relevant. Grano says
The puzzling distribution of case in English coordinated pronouns has sparked a number of attempted
Some explanations take case variation to be syntax-internal, and among these, some ...
I strongly recommend looking at systemic functional linguistics. SFL can offer a few different perspectives. At the syntax level, which SFL calls lexicogrammar, it would be useful to look at the use of the nominal group structure. At another level, which SFL calls discourse semantics, it would be useful to look at the system of reference e.g. https://books....
The subdomains of discourse analysis, dialogics (Bakhtin), and the study of narrative discourse markers (Labov & Waletzky) may be of interest.
There is significant literature on this topic, so you can start by googling some of the concepts above.