To return to this debate fifteen years later... :)
The portrait on page 6, panel 3, of "Crystal Balls" (page 3, panel 10 of "Calculus Affair") is of a man in a short wig, the sort usually associated with the late-18th century. Such wigs were worn by men like George Washington or James Cook who were born in the 1720s or 30s. If he is a son of Sir Francis then he was born rather late in life - I imagine Francis being in his thirties at the time of his adventure with the pirates (1698 in the original French).
The one on page 51, panel 8, of "Crystal Balls" is dressed in the manner of an well-to-do man of the mid-17th century with the sort of wide-brimmed hat that was common at the time. He looks like a cavalier, a period more associated with Charles I of England or Louis XIII of France. Feels more like before the period of Haddock's ancestor.
The one on page 53, panel 10, of "Crystal Balls" is wearing a large wig and fashionable clothes of the sort that many upper-class people would have worn in the early 18th century. He could be a Hadoque of the generation after Sir Francis, dressed in the way he would go to a court like Versailles. He, at least, could be one of the sons.
This presumed second son of de Hadoque (page 53 of "Crystal Balls") is holding a book. If it's a Bible, this may explain the chapel in the basement of Marlinspike.
Not necessarily. Some people would include books in their portraits in order to show that they were well-educated and well-read.