Are there any modern accounts (either of personal experiences of individuals on this forum, or in general) of an individual creating their own language and teaching it to their child(ren)/family?
One guy taught his daughter Volapuk.
There is a contemporary case of someone teaching their kids their personal conlang, she used to be active on one of Facebook's conlang groups.
The revived languages, Cornish, Hebrew, Sanskrit, have similar dynamics to conlangs. Having government support in the form of schools and day care works wonders for the project being successful.
Getting a child to speak your languages takes time (20+ hours a week) of exposure, and it really helps to have a community of peers who also speak that language, or a child's decision to keep using their parents language will be personal and idiosyncratic. I get this impression from people I've met who tried speaking Arabic or Icelandic to their kids in the US where they got plenty of exposure to their parents, but no particular supporting community of peers.