Sort of what tropes to avoid,

With only 2,000 words, the parents do not need to be in the story at all unless they are critical to the conflict. Not necessarily a specific to SF, but when I read something that short, I hate when authors try to cram in too many characters - it gets confusing. Perhaps others will have some better suggestions for you that are specific to SF.

Yes, the amount of YA and kids books where the parents have mysteriously been removed so they can't come in and help the MC's (or stop the fun!). To be honest, it's gonna seem like a trope whatever reason you give. So, what about one where the parents are there, but they're so wrapped up in their own problems that they currently would barely notice their kid was on fire? Not necessarily a bad problem; it could simply be that they're pulling 100-hour weeks to get past a critical stage of a problem at work. (critical failure of life-support systems on a colony? Attempting to jury-rig a solution to hold until the ordered part arrives in 2 months time?) Or you could just have crap parents, period - ones that would be the last persons the MC's would go to with a problem. Lastly, you could have the MC's raised in an 'unconventional' way; might be that now all kids are raised communally, but the place is so short-staffed that the MC's can slip off for hours at a stretch?

In my opinion, the problem with tropes generally isn't any one specific trope in and of itself; it's what people do with them. Finding an interesting and unique way to spin something isn't easy, but it's often worth it. Whether that's by 5 degrees or 180.

You're dealing with short fiction, which means you really don't have a lot of room to play around. I think the first thing to consider is 'what is important' in your story. I know there is a lot of stigma against absentee parents in YA novels. Not sure how / whether that translates to something under 2k words.

But... Let's see. Reasons or logics to include or deal with parents (for fun):

-- MC is somewhere parents aren't (i.e. a training academy)
-- MC has been separated from family in an emergency
-- MC cannot tell parents a key detail out of fear / embarrassment / to protect them etc.
-- MC's parent(s) are the antagonists
-- MC is on a quest to rescue parent(s)
-- MC has an ability that parents do not and has become obligated to complete a quest or task out of societal necessity. Parent(s) may or may not approve / support.
-- Parent is with MC at the beginning of quest but something happens part through that requires MC to step into a larger role than expected.
-- MC's colony / race / etc. are hatched from eggs and raised communally
-- MC does not know real parents b/c they were conceived outside the social norms of their society
-- MC does not know real parents as s/he was taken from them shortly after birth.

The list could go on and on. But you get the idea, right? I hope this helps.

You could just have it that the mother is trying her best not to notice; after all, the easiest way to deal with a problem is to pretend one does not exist...

And, if this is a short piece, what's the time-frame? It's more reasonable that the parents might miss something for a day than they be blind to it every day for a week, for example. A busy woman, on a busy morning, might not look that closely at her daughter's head. Especially if the girl doesn't keep touching it, or otherwise drawing attention to it.

Important point: Portable ear jack - how big and how obtrusive is it? And how portable? Can she take it out until she's out of the house? How about she does her hair differently, tells her mother she's just trying the style out, or, if cyber-space ear jacks are a hot thing, how about kids who can't have one buy imitations? Or, if the jacks are forbidden or controversial, people started wearing strange hats to cover them, and the hats themselves became a fad?
Maternal sigh. "Can't you take that stupid hat off, it makes you look like a wire-head, and it hides your pretty face!"
"But, Ma, everybody's wearing them!"