I completely agree about finding it hard to follow too many ongoing storylines. I tend to have one overall household storyline that the different members dip and and out of and when they’re not centre stage I tend to leave them on auto or skill building.
I don’t usually play teen sims, but for the ones I do have stories in mind for, their parents are kind of background characters so they don’t have anything exciting going on other than surviving and going to work.
But to actually answer the question I usually wait for the young adult stage to move out children, with the exception of one teen who I had run away and live in a tent in a residential park lot.