Can we sue the BBB for an arbitration decision that helped their "client"?

In my previous question, asking what to do about the decision made during arbitration against a flooring company, What can we do if we KNOW, the decision was wrong?

I understand that any arbitration hearings in Texas are binding, yet what can we do if we do not agree with the decision? In speaking to 2 experts, on who is "responsible" for installing a laminate floor and presenting this evidence, I do not feel that the arbitrator did the proper research. Even I, not the legal expert, know that when a company is hired by the contractor to do a job, it is there responsibility to do the job right. We had all evidence presented and even the contact I had with the BBB did not understand until she "personally" spoke with our expert. Heck, even the business owner admitted to not properly installing the floor under oath! She said that it was because she was a "woman" and that she was not a person who could handle confrontation so she ignored our request to fix our floors etc.

I strongly believe, that the arbitrator in this case, did not do his research properly and therefore hurt us by his decision. We now are stuck with $21,000 dollars in damaged flooring that will hurt us in the future selling of our home. - Is this your question? Add additional information