If he misses the first prayer in congregation in the mosque, should he pray with his family or should he come to the mosque for the second prayer in congregation?

Prayer in congregation in the mosque is obligatory for men
who are able to do that, if they can hear the call to prayer, as has been
explained in the answer to questions number
120 and
8918. 

If a person comes to the mosque and finds that he has missed
the prayer in congregation, it is prescribed for him to pray in congregation
with others who also missed it, or with other worshippers who pray with him
as an act of charity, because of the reports narrated by Abu Dawood (574)
from Abu Sa’eed al-Khudri (may Allaah be pleased with him) that the
Messenger of Allaah (blessings and peace of Allaah be upon him) saw a man
who was praying alone, and he said: “Will any man be charitable towards this
one and pray with him?” The hadeeth was classed as saheeh by al-Albaani in
Saheeh Abi Dawood. 

If he knows that the congregation in the mosque has ended and
he is in his house, then he may pray with his family or he may go to the
mosque to offer the prayer there with the second congregation. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy upon him) was
asked: What is the ruling on having a number of prayers in congregation in a
mosque which has a regular imam and a regular muezzin? 

He replied: Having a number of congregations is divided into
two categories. The first category is when that is done regularly so that
the second congregation deliberately comes late in order that a second
congregation may be done. This is an innovation, because only one
congregational prayer should be done in the mosque. 

The second category is when that is not done regularly and
deliberately, but after the first congregation ends some other people come
into the mosque and they offer their prayer in congregation. This is
prescribed and is Sunnah, because the Prophet (blessings and peace of Allaah
be upon him) was with his Companions one day, and a man came in who had
missed the prayer, and he said: “ Who will be charitable towards this man
and pray with him?” and one of the Companions got up and prayed with him. 

And because the Prophet (blessings and peace of Allaah be
upon him) said: “A man’s prayer offered with another man is better than his
praying on his own, and his praying with two other men is better than his
praying with one other man. The more there are the more beloved it is to
Allaah.”  

With regard to the notion held by the people that having a
second prayer in congregation is an innovation, that is correct if it is
done regularly and deliberately. But if it happens occasionally, then having
a second prayer in congregation is Sunnah, because of the command of the
Prophet (blessings and peace of Allaah be upon him and his family). 

Question: Even if it is done in the house after the first
prayer in congregation has ended? 

Shaykh: No, in the mosque is better, because if it is done in
the mosque the size of the congregation may increase and people who come
later may join it, so that will be better. Moreover, sometimes people go
from their houses to the mosque in order to pray with the congregation, but
they may miss it and find that they have already prayed, in which case
praying in the mosque is better for him and others, because if he and his
companion return home and offered a prayer in congregation there, another
person may come after the first prayer in congregation has ended and find no
congregation, so he misses out on praying in congregation. So it is better
for it to be in the mosque. 

Yes, if we assume that he knew when he was at home that the
prayer in congregation had ended, then in this case we say: It makes no
difference, pray in your house, because if he goes out to the mosque he may
feel embarrassed to meet people when they are coming out from the prayer, so
he may pray in his house. 

But if he has come and entered the mosque, and found that
they have already prayed, he should not leave. Rather he should pray with
the congregation in the mosque. End quote from Liqa’ al-Baab al-Maftooh,
41/12. 

A congregation may consist of two people, an imam and one who
prays behind him. If a man is excused for not praying in congregation or he
has missed the prayer in congregation, and he prayed with his wife, then
this is a congregation and his wife should stand behind him.

See also the answer to question number
98739. 

And Allaah knows best.