I agree Khan likely had no actual children. If that were the case, he'd call them by their names, or pay a little less attention to Joachim.
If memory serves, wasn't To Reign in Hell the final installment of the excellent Khan Trilogy?
Indeed! Glad you liked them.
I spoke with Judson Scott (who played Joachim) at a convention once. He believed that Joachim was indeed Khan's son and that's how he played him.
Since this had never been "officially" established, I split the difference and made him Khan's foster son in the book.