Praying in congregation is obligatory for every adult man who is able to go to the mosque and who hears the call to prayer.
What is meant by hearing the call is that a person can hear the adhaan given in a regular voice without amplification of the sound, if the muezzin (caller to prayer) raises his voice and there is no wind or other noise that could affect hearing it.
This has to do with the five daily prayers in congregation. With regard to Jumu’ah (Friday prayer), that is a different matter. It is obligatory for everyone who is in the city or town in which Jumu’ah prayers are held regularly, whether he can hear the adhaan or not, not matter how spread out the city is. See also the answer to question no. 89676
Based on this, if the mosque is so far away that you cannot hear the call, you are not obliged to go and pray in congregation in the mosque, and in that case you can pray with your family.
But if you can hear the call, it is obligatory to pray in congregation, and it is not permissible for you to forego that in order to make sure that your family members pray, because this is forsaking an obligatory duty for something that has to do with others and that can be achieved by other means, such as following up with them and asking them after you come back from the mosque.
When a boy reaches puberty he becomes accountable, but this does not mean that the parents are no longer obliged to advise him and enjoin what is good and forbid what is evil, especially if the boy is living with them. Allah says (interpretation of the meaning):
“O you who believe! Ward off yourselves and your families against a Fire (Hell) whose fuel is men and stones, over which are (appointed) angels stern (and) severe, who disobey not, (from executing) the Commands they receive from Allaah, but do that which they are commanded”
And the Prophet (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…” Narrated by al-Bukhaari (853) and Muslim (1829).
And he (blessings and peace of Allah be upon him) said: “There is no person whom Allah puts in charge of others, and when he dies he is insincere to his subjects, but Allah will forbid Paradise to him.” Narrated by al-Bukhaari (6731) and Muslim (142).
Part of this responsibility is that the father should not bring any evils in the house or allow them if his son brings them in, such as if he wants to bring indecent satellite channels, for example. In that case it is the father’s duty to refuse that and resist it, because that is going on in his house for which he is responsible. But if the son moves to his own place and does that, then the father’s duty is to offer advice and reminders with wisdom and beautiful preaching.
We ask Allah to guide and help us and you.
And Allah knows best.