If any of the signs of puberty appear in a boy, he becomes accountable

Firstly: 

Puberty is reached when one of three things happens in the case of males: 

1.Wet dreams

2.Growth of coarse hair in the pubic area

3.Reaching the age of fifteen

If one of these three things occurs, then the individual has reached puberty. In the case of females there is a fourth sign, namely the onset of menstruation. 

Please see the answers to questions no. 20475, 138738 and 192334 

Secondly: 

With the onset of puberty, the individual becomes subject to shar‘i rulings that apply to him, so he should not shake hands with women or look at them, and he should not be alone with a woman, because he has now become accountable and the things that are prohibited for adult men are also prohibited for him, because he is one of them. It is not permissible to be careless about this matter, and it is essential to take it seriously. So you must refuse to go to the women’s prayer hall, and refuse to shake hands with non-mahram women or look at them, including your cousins, even if they object to you doing that, because there can be no obedience to any created being if it involves disobedience towards the Creator. 

You can seek the help of your sister, for example, or other mahram family members to explain the shar‘i teachings to your cousins. As you are taking this matter seriously, they will have to understand. 

Similarly, if your father or mother tells you to go in to where the women are, or to shake hands with them, it is not permissible for you to obey them; rather obedience is only with regard to that which is right and proper, but if it involves sin then there is no obedience to anyone. 

There is nothing wrong with you explaining to them that you have reached the age of puberty and are now a man, so the same things are haraam for you as are haraam for men. But this explanation should be given politely and gently. 

You could also seek the help of one of your relatives in that regard. 

Please see the answers to questions no. 45905 and 104165 

Fourthly: 

If a fourteen-year-old boy has not yet reached puberty, he is very close to it, and such a person should not be allowed to see women’s ‘awrahs. Women have to understand that and observe hijab in the presence of one who is very close to puberty. 

Allah, may He be exalted, says (interpretation of the meaning):

“and not to show off their adornment except only that which is apparent (like palms of hands or one eye or both eyes for necessity to see the way, or outer dress like veil, gloves, head-cover, apron, etc.), and to draw their veils all over Juyubihinna (i.e. their bodies, faces, necks and bosoms, etc.) and not to reveal their adornment except to their husbands, their fathers, their husbands fathers, their sons, their husbands sons, their brothers or their brothers sons, or their sisters sons, or their (Muslim) women (i.e. their sisters in Islam), or the (female) slaves whom their right hands possess, or old male servants who lack vigour, or small children who have no sense of the shame of sex”

[an-Noor 24:31]. 

Ibn Katheer (may Allah have mercy on him) said: “or small children who have no sense of the shame of sex” that is, because they are so young, they do not understand anything about women and their ‘awrahs, such as their soft speech or alluring ways of walking and moving. If the child is small and does not understand such things, then there is nothing wrong with him entering upon women. But if he is adolescent or close to adolescence, such that he understands these things and can distinguish between who is unattractive and who is beautiful, then he should not be allowed to enter upon women.

End quote from Tafseer Ibn Katheer (6/45-46) 

It was said to Imam Ahmad (may Allah have mercy on him): When should a woman cover her head in front of a boy? He said: When he reaches the age of ten years.

End quote from al-Mughni (7/100) 

With regard to reaching the age of fifteen years, what is meant is that the boy has completed fourteen years and has entered his fifteenth year. This is often applicable to one who says that he is fourteen years old; he has completed fourteen years. Therefore this sign of puberty is applicable in his case. 

Moreover, the years that count in this matter are Hijri years, not Gregorian. This means that his age will be less than if it is counted by Gregorian years. 

The guideline on puberty in your case is that you have reached this age, which will help you to avoid embarrassment when speaking to your family or your relatives, because there is nothing embarrassing about reaching a certain age. 

Your cousins have to understand the shar‘i ruling. It is not permissible for them to uncover in front of you or to shake hands with you, because you have reached puberty. By the same token you must not obey them by disobeying Allah with regard to shaking hands with them or going to the women’s prayer hall. 

Your father has to understand that, and you have to be firm about this matter, for Allah is not too shy to speak the truth. There is nothing wrong with speaking frankly when necessary about puberty, and explaining that it is not permissible for you to shake hands with women or enter upon them. 

And Allah knows best.