Basic Trope: A child shows a level of maturity significantly beyond that expected of their age group.
Straight: Alice is able to manage a shop for a while while her father is out buying groceries/saving the world, and keep her younger siblings in line, despite being only thirteen. And she still completes her homework on time and gets good grades.
Double Subverted: Alice appears to be abandoning her post in the shop to play with her friends, but as soon as the kids are out of sight they start planning how to stop the Diabolical Mastermind from taking over the city.
Conversed: "You know, from watching this show you'd think that adulthood begins at ten."
A fourteen year old Alice is forced to take on a job and keep a household due to one of her parents being insane and the other missing, and the state she lives in having no child support services. For a while she manages to balance her job, chores, her own and her siblings education and care for her parent, possibly while avoiding myriad dangers, but the pressure ultimately gets to her and she suffers a breakdown, becoming violent and turning to drink.
Alice's maturity causes her to be a Fish out of Water with everyone; her maturity causes her to have significant problems relating to and making friends with her peers, and people who are more in line with her maturity (I.E. adults) refuse to take her seriously because she's so young.
Alice shows extremelyTroubling Unchildlike Behaviour due to her excessive understanding of how the world works and all the necessary evils society needs in order to operate. This can range from apathy towards mass murder all the way to being able to commit murder with a good justification.
Alice damn well knows she's wise beyond her years and isn't afraid to flaunt that at every opportunity, which eventually causes her to develop a massive superiority complex.
Alice is forced into the above situation, but just before Alice snaps completely the family starts to get helped by the community, her siblings start chipping in and eventually some sort of equilibrium is formed where Alice is still dealing with adult responsibilities, but has enough support from friends and family to avoid being unable to deal with them. The fact she's growing up is helping as what was nearly impossible at fourteen is a merely very hard and stressful at fifteen.
As she is shunned by her peers for being more mature than them, she finds friends in older people, who accept her intelligence.
Played For Laughs: Alice is by far the youngest of the Ragtag Bunch of Misfits yet while they're all running away from the yeti, she's the one who calmly recognizes that its a statue.
Played For Drama: Alice is left to look after her siblings and her insane remaining parent, and is forced to handle things that would be strenuous even for adults.