Is the urge to stop praying for a fiancé rejected by his family because he is divorced and has children—due to the fact that istikhara indicated the father's rejection—a satanic whisper or an inner feeling from God that the matter will not be completed?

If your suitor is a man of religion and good character, continue to supplicate to Allah to facilitate your marriage to him. It is better for the supplication to be general, "O Allah, grant me a righteous husband," because this obsession might be from Satan to cause you despair.

The fact that the suitor has been previously married or has children is not a legal impediment according to Sharia. So, continue trying to convince your parents. If they insist on refusing and you fear being wronged, then you have the right to take the matter to the Sharia court.