Yellowstone did not show the actual moment where Beth told her father, but the truth that John learned went back to when Beth was 15 and she went to her slightly older brother Jamie for help getting an abortion.
Jamie procured one for her at a secret cost, in that he did not tell Beth that Indian Health Services required abortion patients to be sterilized.
Kevin Costner’s John seemed to be reaching his breaking point regarding Beth’s attitude with Jamie when he finally asked her point-blank what Jamie did to deserve her ire.
Hence, Beth has long been angry at her brother for taking away her ability to have children, all without her authorization.