All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Firstly, one’s grandmother is one of his origins, and she is like the mother. Being kind and dutiful to the grandfathers and grandmothers is like being kind and dutiful to the parents. Ibn Muflih said in Al-Aadaab Ash-Shar’iyyah, “The scholars agreed that being kind and dutiful to one's parents is an obligation, and they also agreed that being kind and dutiful to one's grandparents is an obligation.”
Besides, Al-Hattaab said in his book Mawaahib Al-Jaleel, “AI-Ikmaal reads at the beginning of the Chapter 'Dutifulness and Prayer' that dutifulness to grandparents is the same as dutifulness to parents.”
Secondly: It is Islamically required to take the initiative to do good and to hasten in doing it, Allaah says (what means): {And hasten to forgiveness from your Lord and a garden as wide as the heavens and earth, prepared for the righteous.} [Quran 3:133] This is more emphatic in regard to the prayer, as it is the best kind of goodness. Thawbaan narrated that the Prophet said, “Adhere to righteousness even though you will not be able to do all acts of virtue. Know that the best of your deeds is the prayer and that no one maintains his ablution except a believer.” [Al-Haakim and al-Bayhaqi]
Hence, you should not delay the prayer because of anyone, especially if it entails that you miss some rak'ahs (units of prayer) with the imaam. Also, going early to the mosque is of great virtue, as one achieves the virtue of waiting for the prayer and getting a place in the first row. Abu Hurayrah narrated that the Prophet said:
“If people knew what is (i.e. the great reward) in the athaan and praying in the first row and they did not find a way to achieve it except by drawing lots, then they would do so, and if they knew what is (i.e. the great reward) in Tahjeer (i.e. going early to the prayer), then they would compete with each other, and if they knew what is (i.e. the great reward) in the ‘Isha and Fajr prayers, then they would come to them even by crawling (if they cannot walk).” [Al-Bukhari, Muslim and others]
An-Nawawi said in his commentary on Saheeh Muslim, quoting from al-Harawi and others: "His [Prophet’s] saying, “And if they knew what is (i.e. the great reward) in Tahjeer, they would compete with each other…” Tahjeer means going early to the prayer, any (congregational) prayer whatsoever..."
Moreover, you should help your cousins to perform the prayer in congregation, and if you go early with them to it, then you will get a reward of guiding people to do good and helping them in it.
Thirdly, enjoining good and forbidding evil is something Islamically required, and it is one of the communal obligations, but it may become an individual obligation if one is in a situation where there is nobody else to do it. For more benefit, please refer to fataawa 29987 and 84348. So if you see someone who does not pray, for example, or someone who is lazy in going to perform the prayer in congregation – which is an obligation according to the preponderant opinion – without having a sound excuse, then you are obliged to object to him and enjoin him to do good. There is a great reward in doing so and in calling people to Allaah. Abu Mas'oud Al-Ansaari narrated that the Prophet said, “The one who guides people to do something good will have a reward similar to that of its doer.” [Muslim]
Finally, a bad relationship with some people does not Islamically prevent from enjoining them to do good and forbidding them from doing evil, noting that the sharee'ah prohibits cutting ties between Muslims and plotting against each other, and it orders friendship and having good relations. Abu Hurayrah narrated that the Prophet said, “(O Muslims) Do not envy each other, do not hate each other, do not spy on each other, do not be hostile to one another (standing back to back), do not overbid against each other (in trade); rather, O servants of Allaah, be brothers.” [Al-Bukhari and Muslim]
For more benefit, please refer to fataawa 86772 and 86090.
Allaah knows best.