Is a father who unintentionally saw his son's private parts, then immediately averted his gaze, sinful, given that he felt a trace of lust which was not by his choice, and is this considered unlawful gratification?

The ruling on looking at the 'awrah is the same for a son and others, which is prohibition. As long as you avert your gaze from it, there is nothing upon you. Do not pay attention to satanic whisperings, and completely disregard them.