It is not permissible for a girl to wear short clothes in front of her parents under any circumstances

Firstly: 

There is no doubt that good behaviour with parents, honouring
them and treating them kindly are good deeds for which a person will be
rewarded in this world and the hereafter. 

However, there is no obedience to them if it involves
disobedience to Allah and His Messenger, and one should not seek to please
them by angering Allah and incurring His wrath, and going against His
command and the command of His Messenger.

 Secondly: 

With regard to what a woman may wear in front of another
woman, what is prescribed is for her to cover the area between the hand and
ankle, but if a woman needs to roll up her garment for the purpose of work
and the like, then she may roll it up to the knee, or if she needs to roll
up her sleeves, she may roll them up to the elbow. But she should do that
only as much as is necessary; it is not permissible for this to be her usual
way of dressing. 

It is permissible for a woman to cover in front of her
mahrams what she may uncover in front of other women; she may uncover her
head, neck, foot, hand, forearm, leg and so on. 

But despite that she should not make her clothes short,
coming only to the knee and the like, let alone making it shorter than that.
Rather she may uncover only what is ordinarily uncovered of the lower leg,
the foot, and the like. 

She should not wear these tight clothes that show the shape
of the ‘awrah or display her charms, even if that is in front of her mahrams.
Rather she may only do that with her husband. 

See the answers to questions no.
6569
and
12371

What we advise the questioner to do in light of the
circumstances that she mentions is the following: 

-She should try to explain
the Islamic rulings to her parents in a proper and clear manner, by telling
them about the shar‘i evidence and what the scholars said. She can help
herself to do that by using available means such as tapes, lectures, books,
fatwas published on trustworthy websites, and the like.

-She should handle this
matter with the utmost gentleness, wisdom and patience, even if that causes
her some distress and pressure.

-She should try hard to
explain the wisdom behind modesty, even at home with her parents, so as to
highlight the beauty of Islamic teaching and so that her parents will
understand the divine wisdom behind that.

-She should explain to her
parents that the basic principle behind what she is doing is obedience to
Allah and to His Messenger (blessings and peace of Allah be upon him), and
it is not intended to cause hardship to herself or to make her parents angry
with her.

-She should offer a lot of
du‘aa’ (supplication) and turn to Allah, may He be exalted, asking Him to
guide her parents, to divert harm and annoyance from her and to enable her
to do that which He loves and is pleased with. 

Moreover, we think that the questioner should try hard to
save whatever she can of her personal income so that she can buy clothes
that will help her to cover up at home. She does not have to change all of
her clothing completely rather in the beginning she may stick to what is
absolutely necessary. 

We suggest that she should have a “prayer suit” or the like
that she can put on when any of her mahrams come, if she is wearing
something that is not appropriate. 

And in all of that, she should strive to fear Allah and do
her duty towards Him by doing that which He is pleased with and refraining
from that which incurs His anger and that He has forbidden, as much as she
can, and Allah does not burden any soul with more than it can bear. 

And Allah knows best.