I believe you have a truly valid complaint here and I hope you get a response from United. I will warn you, however, that I doubt they will send you complimentary round trip tickets. More than likely you will receive vouchers good for a certain amount off a future flight. These vouchers are full of restrictions and usually end up costing more than a discounted flight would cost.

Just a small critique on your letter, it is best to leave out the sarcastic remarks like "great customer service. LOL". It does take away from an otherwise great letter.

Good luck getting this resolved.