All in the Family
Based on our above introduction, there is no apparent reason for Yitzchak to assume that only one son is to be chosen and the other rejected. Unlike Yitzchak and Yishmael who come from different mothers, both Yaakov and Esav are born from the same mother. In fact, they are twins! Therefore, it is only logical for us to presume that Yitzchak assumes that both Yaakov and Esav are chosen (Board #2).
Furthermore, even if there is some divine reason to choose only one son, it should be God's choice and not Yitzchak's! After all, up until this point, God alone had been involved in this bechira process. He had chosen Avraham, and He alone had chosen Yitzchak over Avraham's other offspring. Without a specific divine command, why would Yitzchak even consider making such a bold decision?
However, if indeed both Yaakov and Esav are considered chosen, why does Yitzchak intend to bless only one of them?