@Freya
I don't keep up with the Trump family, but it seems to me I remember Don Jr. and wife have a "fairly new" baby and several other children. I don't know if the children are old enough to read the paper or if Dr. Jr and the wife separately, even get a newspaper. If old enough to use the internet, that is the more likely place they would read it.
I would hope the mom and dad are keeping the underlying details to themselves and not involving the children. However, in divorces, sometimes the dad and mom try to get the children to "choose" which parent is "right" and which is "wrong". Hopefully, they are smart enough not to do this so the children will continue to love both parents since they will be with both parents all their lives.
I have no reason to believe the parents aren't doing the best they can for these kids...they're probably not fighting over visitation and child support (because of their wealth). However, the Media loves these bedroom stories, and can be counted upon to splash this story everywhere, and if the children are old enough to read and surf the web, they will see them.
Add to that the fact the press haaaaates Don Jr's father, and you can guarantee this divorce will get lots of extra coverage. Since they are convinced as some are Donald Trump Sr. is guilty of everything he's been accused of (and more), they will add to the smears against the family because Trump.
Being careful with the coverage to spare children only applies to Democrats like Chelsea Clinton.