The husband is the priest of the family. But not the presbyter

A priest is one who offeres a sacrifice. A husband must sacrifice himself to service his family and protect and foster the spiritual life of the family. How this is appropriate depends on the family. It might mean taking the lead in speaking openly about limits on the secular in the house (preventing tv from intruding into prayer time). It might mean setting an example. It depends on whether the wife and children are faithful Christians, willing to follow if the husband leads in the Lord... or of another religion entirely. Wisdom and the guidance of a Father in Confession is essential.
Ideally, families should pray the Agpeya together, read the Bible together, talk about its meaning together. Normally the husband would lead the Agpeya prayer. The husband is ultimately responsible for the spiritual life of the family, and will answer at judgement for failing to properly care for it. Unfortunately though, more often the husband does not lead, and many pious wives pick up the role, leading the children while the husband is too busy.
The husband is not though, the Father in confession for the family. The hidden, personal prayer lives of the family are just that, personal, and should only be exposed to the Father in confession. Any temptation to critique the priest's rules of prayer for the other family members, or to make sure they are following them, must be resisted. Each person must have their own interior spiritual life, that is supported by the family prayers, not replaced by them. Finding the correct balance between supporting and not over-burdening is important.
In the EO traditions, I believe the husband may bless his children, but with his fingers held together, as he would cross himself, not the way the priest holds his hand. I am not aware of any such tradition in the Coptic Church. Also, in the EO tradition incense is offered in the house along with prayers. This is strongly discouraged in the Coptic tradition. An oil lamp by the icons is nice, and perfectly acceptable though.
If it is impossible to make it to Midnight Praise at the Church, this can be said in the home (as can the Vespers Praise and the Doxology of Prime, which are shorter). It is nice to follow a calendar, and to be aware of the seasons and feasts of the Church, especially if it is not possible to attend the weekday Liturgies. A short veneration for the saint of the day can be said in the home. It is nice to follow the seasonal variations for "He has {come/been born/Risen/been Baptised/been crucified} and saved us", and variations around the feasts for the verses of the Trisagion when praying the Agpeya together.
I think that the most important way to live Orthodox Christianity in the home though is through virtue, by loving your family. Marriage is an opportunity to destroy the self will by subjecting it to the needs of your spouse and children. This is training for subjecting our wills to God's. Having love in the family is greater than any formal prayers together. If one is feeling proud, or joy in controlling or directing others when leading family prayers, then a remedy must be sought through confession, and probably delegating more to the other family members to yield control. Great care must be taken because Satan will attack such good works and try to twist them into something harmful.