What is correct pronoun usage in this sentence. Her and your brother enjoy debating about politics?

Here is a good grammar rule to remember:

make a sentence simple and the answer will often magically become clear!

When more than one person is mentioned in a sentence, cross off the other person and see if the sentence makes sense.

(Use your ear!)

So, cross off “and your brother.”

Her enjoy(s) debating?!

No way!

SHE enjoy(s) debating!

Therefore, the sentence should read, “She and your brother enjoy debating about politics.”

On a more technical note, a pronoun needs to be in the nominative case (I, we, you, he, she, it, they, who) when serving as the subject.