How to parse "which was especially humiliating because everyone was talking about it the next morning"?
Solution 1:
One way to parse is to rearrange or separate clauses, and see events on a timeline. See if this helps:
1) Cara's mother berated her in front of the entire basketball team. 2) Everyone was talking about it the next morning. 3) That (#2) was especially humiliating (for Cara).
Solution 2:
Cara’s mother berated her in front of the entire basketball team, which was especially humiliating because everyone was talking about it the next morning.
Cara’s mother –subject
berated – verb
her – object
in front of the entire basketball team, - adverbial phrase modifying “berated”
which was especially humiliating – subordinate conjunctive relative clause whose referent is the main clause (cf "and that was especially humiliating")
because everyone was talking about it the next morning. - Subordinate clause of reason modifying “humiliating".