Is it a conflict of interest to go to arbitration against a company for a full refund on an outdoor surface we purchased and collect on an insurance claim on the same surface because of damage from a hail storm?
No. Basically, a "conflict of interests" exists when one represents two or more parties to the same dispute whose respective interests conflict. First, you are not representing anyone. Second, you do not owe any legal duties to either the seller of the surface or the insurance company. Therefore, none of the essential elements of a conflict of interests is disclosed here.
The above said, it does not follow that you can permissibly collect twice for the same loss you have suffered. Depending on facts not disclosed by your post, your case against the seller may be barred, in whole or in part, by the election of remedies doctrine, the "one satisfaction" rule, or some form of equitable estoppel. However, these affirmative defenses are for the seller's benefit, not yours, and the seller is obligated to assert and prove them in the arbitration. Also, if the insurer has already paid your claim, it insurer may have subrogation rights to all or a portion of your recovery, if any, against the seller.
Since you are going to arbitration, I presume that you have a lawyer. If so, you should pose your questions to him or her, as he or she is in the best position of anyone on the planet to be able to answer them correctly. If you do not have a lawyer, I suggest that you hire one right away. Handling an arbitration is not a DIY project for a non-lawyer. It is only slightly less complex and difficult than trying a lawsuit.
The Texas collateral source rule protects the ability of insureds to collect judgments against tortfeasors without suffering any reduction in property damages. But check your insurance policy - it will likely give the insurance company lien, assignment, or subrogation rights to any recovery you might receive from the arbitration.
This general opinion DOES NOT create an attorney-client relationship. No communication can ever replace the specific advice of a lawyer. Each person's situation is different, and additional facts can change legal outcomes. You should consult privately with a lawyer if you have a question about a legal dispute.