She is asking how she can teach her mother and sister about the rulings on tahaarah (purification)

Firstly: 

There is no doubt that teaching children
what they need to know about their religion comes under the heading of
obligatory education and care that Islam has enjoined upon parents towards
their children. Allah, may He be exalted, says (interpretation of the
meaning): “O
you who believe! Ward off from yourselves and your families a Fire (Hell)
whose fuel is men and stones”
[at-Tahreem 66:6]. 

Mujaahid (may Allah have mercy on him) said:
Fear Allah, and advise your families to fear Allah. 

Qataadah said: He should instruct them to
obey Allah and tell them not to disobey Allah, and he should discipline them
in accordance with the teachings of Islam, and he should enjoin them to
follow the teachings of Islam and help them to do so. If you see any act of
disobedience towards Allah, then you should make them stop it and rebuke
them for it. 

Something similar was stated by ad-Dahhaak
and Muqaatil: It is the Muslim’s duty to teach his household, both his
family members and his servants, what Allah has enjoined upon them and what
Allah has forbidden to them. 

Tafseer Ibn Katheer,
8/167 

The Messenger of Allah (blessings and peace
of Allah be upon him) said: “Each of you is a shepherd and each of you is
responsible for his flock. The ruler of the people is a shepherd and is
responsible for his flock. A man is the shepherd of his household and is
responsible for his flock. A woman is the shepherd of her husband’s house
and children and is responsible for her flock.” Narrated by al-Bukhaari
(853) and Muslim (1829). 

He (blessings and peace of Allah be upon
him) also said: “Your child has a right over you.” Narrated by Muslim
(1159). 

An-Nawawi (may Allah have mercy on him)
said: ash-Shaafa‘i and his companions  (may Allah have mercy on them) said:
Fathers and mothers are obliged to teach their children that which will be
obligatory upon them when they reach puberty. So the parent or guardian
should teach them how to purify themselves, how to pray and fast, and so on;
they should teach them that fornication and adultery, homosexuality,
stealing, consuming intoxicants, lying, backbiting and so on are all haraam;
they should teach them that once they reach puberty, they will become
accountable, and they should teach them how to recognize when they have
reached that stage.

End quote from al-Majmoo‘. 1/26; see
also al-Majmoo‘, 3/11 

Secondly: 

If your mother does not know the rulings
connected to reaching puberty, as often happens in places that are far away
from knowledge and scholars, such as desert regions, Western countries, and
so on, then the mission of teaching and calling people to Allah must be
undertaken by whoever in the family has that knowledge, whether that is a
boy or girl, the closest, then the next closest. 

So long as you have some knowledge of the
Islamic rulings that are needed, and you know that your sister is about to
reach puberty, then you must teach her what she needs to know of these
rulings, and you should choose the best and most appropriate way of doing
so. 

In fact, we think that your teaching her may
be more beneficial and easier than the mother teaching her, because of your
closeness in age and because you will understand one another easily. 

Then you should also teach your mother what
she needs to know of religious rulings that you think she does not know. 

You can also seek help in doing that, along
with direct teaching, by telling your mother about beneficial Islamic media
channels, such as trustworthy educational websites and good Islamic
satellite channels that follow the way of Ahl as-Sunnah, if there is
something that will benefit your family in a language that they know. 

There is no need for any shyness or the like
in any of these matters. There are still people who do not know many rulings
that they need to know, and the one who knows them is obliged to help them
to learn them, whether they are young or old. 

It was narrated from Zaynab, the daughter of
Umm Salamah who said: Umm Sulaym came to the Messenger of Allah (blessings
and peace of Allah be upon him) and said:
O Messenger of Allah, Allah is
not too shy to tell the truth. Does a woman have to do ghusl if she has an
erotic dream?…

Narrated by al-Bukhaari (130) and Muslim
(313). 

An-Nawawi (may Allah have mercy on him)
said: 

She only said that as an apology before
asking her question, for which there was a need, because it was something
that women usually feel shy to ask about and mention in the presence of
men. 

This shows us that it is appropriate for the
one who has a question to ask about it, and not to refrain from asking out
of shyness. That is not really shyness, because all shyness is good and
shyness does not lead to anything but good, but refraining from asking in
this case is not good, rather it is bad, so how can it be shyness? …
‘Aa’ishah (may Allah be pleased with her) said: How good were the women of
the Ansaar; shyness did not prevent them from understanding matters of their
religion. And Allah knows best.

End quote from Sharh Muslim. 

Thirdly: 

The vaginal secretions that come from women
several times every day do not require ghusl; rather ghusl is only required
in the case of janaabah (impurity following sexual activity) or when a woman
becomes pure following her menses. 

For more information, please see the answer
to question no. 50404. 

See also the answer to question no.
99507 for information on the difference between
maniy, madhiy and other secretions. 

And Allah knows best.