Texas prohibits marriage between first cousin. Although many states generally recognize marriages of first cousins married in a country where such marriages are legal, Texas might refuse to recognize your marriage as it violate the state's public policy.
You may be able to renew your conditional GC based on divorce waiver. The divorce must be finalized before filing the renewal application. Furthermore, you still need supporting docs to prove that the marriage was bona fide marriage. You should hire an immigration to consult your case.