Cheyenne and Charlotte naturally did not believe Bryce's words. The Carters had never truly treated them as a part of the Carter family before, mainly because William Carter was not Dominic Carter's biological son. Thus, Dominic obviously wouldn't let William take over as the head of the family.
William himself did not believe what Bryce said. He grew up knowing that he and Dominic were not blood-related, and Dominic had at best been kind to him and let him join the family on account of his mother. But after his mother passed away, he no longer enjoyed the same treatment that the direct descendants of the Carter family enjoyed. For example, the direct descendants and relatives would receive almost a hundred thousand dollars each year in dividends, while William and his family would only receive about fifteen thousand.
Therefore, Willian didn't believe at all that he would be able to assume the position of the head of the family in the future.