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

Praise be to Allah.

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.