I went back to the salon yesterday afternoon to talk to the owner, Jamie. I was pleasantly surprised to find that Jamie was really attentive and listened to all of my complaints. She apologized for Brenda's behavior and told me that she would talk to her about it later. She refunded half of my total bill saying that she couldn't refund the entire amount since I did receive a relaxer service. After the refund she evened out my hair. I didn't want to argue with her about the amount of the refund since we had that conversation before she started cutting my hair and I didn't want to walk out looking worse than before. All in all she was a hell of a lot more professional than I was expecting considering Brenda's behavior. Jamie also offered me a free service the next time I come in but I definitely won't be going back so I'll never be able to cash in on that.
So a decent outcome to a horrendous initial experience. Thanks to everyone for all of the support on my initial post - it definitely gave me more courage to stand up for myself and go back to the salon.