The Ruling on a Man who Leaves Home for Prayer, but His Children Stay Home

Question :

Is a man allowed to go out for the prayer, leaving his children behind in the house?

Answer:

It is obligatory for a man to abide by the order of Allah mighlig in His saying:
"O you who believe! Ward off from yourselves and your families a Fire (Hell) whose fuel is men and stones, over which are (appointed) angels stern (and) sever, who disobey not, (from executing) the Commands they receive from Allah, but do that which they are commanded."

So it is obligatory for a man to order his family to perform the prayer as the Prophet ordered that in his saying:
"Order your children to perform the Salah when they are seven, beat them (if they don't pray) when they are ten, and separate between them in their beds."

Allâh Almighty also mentioned that Isma'il, the father of the Arabs, used to order his family to pray and give charity, and Allah Almighty was pleased with him.

Therefore, he is not allowed to let his children sleep without waking them up for prayer; even waking them up is not enough, because they can get up and then go secretly back to sleep, so he must make the follow through with it.

In case where he is about to go for the prayer while they are in the house and he fears that the time for the prayer will elapse if he is diligent in waking his children and making sure they stay up, then he should go to the prayer and wake them up when he comes back. He is not doing enough if he is merely quietly calling them to wake up only once or twice and then saying, "I fear I will miss the prayer" and he leaves them alone. It is his responsibility as a father to show them the importance of prayer, and so, if they are slow in waking up, start earlier.

Source:
Ibn 'Uthaimin
Fatawa Islamiyah, Vol. 7 Pages 342-343