WRT children; the infobox templates for modern personalities (e.g Television presenters) tend to specify that children should only be listed of they are notable; for example, [[Michael Douglas]] is listed as a notable child of [[Kirk Douglas]]. But this is because [[Michael Douglas]] is notable in himself, rather than any inherited notabilit; anmd os we list him theree
When we consider inherited aristocratic titles, there seems to be an assumption of necessary notability, as exemplified by examples already given; this, as far as we are concerned, provides historical continuity. The problem is discontinuous inheritance, such as is shown by [[Earl of Salisbury]], and there are worse example to be found.
Back to modern times; should the infobox for [[John Travolta]] mention his children? We had a debate about this a couple of months ago when his son died suddenly; there was nothing notable about him except his parentage, and consensus is that notability is not inherited, so IIRC, although it was mentioned in the JT article, any attempt to create an article about the son, or his death, was quashed.