You say "not about Star Trek
" - do you mean not referencing the ST multiverse that much, or not containing (Starfleet) space travel?
One of the Strange New World
anthology stories is set in an alternate timeline where Star Trek
is regarded "fiction", dealing with a Human boy whose father is a soldier in a 21st century war.
There are also crossovers with other franchises, e.g. Doctor Who
. If you delve into those universes, they'll be pretty unrelated to Trek but you could go on a limp and consider them remote alternate timelines.
If you're looking for family/at home stories, maybe anything related to Lwaxana Troi is your pick.