How to parse "which was especially humiliating because everyone was talking about it the next morning"?

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).

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".