Whether your stepmother's children have any rights in the "joint checking account" depends on matters I am not completely clear about. You state that her children are asking your father
"if they receive half of a joint checking account they shared". I'm uncertain who the "they" are who did the sharing. I think the account was probably shared by your father and his wife, because you refer to him as "the survivor on the account." If that account was a joint tenancy account, your father would receive all money in it as the surviving joint tenant. In that case, her children would have no right to the money in the account.
If the account was not a joint tenancy account, things get murkier. Then who inherits your mother's portion of the account would depend on who she named as beneficiaries of her interest in it, whether by will or other method, such as a pay-on-death bank account. Further, what percentage of the account she owned could be determined by state law. If she and her husband lived in a community property state (such as California), it's likely that each owned 50% of the account. If they lived in a common law state (like New York) each spouse may have owned a different percentage of the account.