Family and the gospel of Jesus Christ are not really two separate things. They are two portions of the same thing.
Nevertheless, a family that is built around the principle of family first may seem sound. But a family must be built around Christ first and foremost. But, and this is crucial, it must be built around Christ knowing that Christ himself will, in the vast number of circumstances, require our family to be our first responsibility in following him.
There is a difference between:
1) a home that puts family first,
2) and a home that puts Christ first, and defines themselves by their church callings and church service,
3) and a home that puts Christ first, and recognizes that to do so almost always means family comes first.
A home that puts family first falls as soon as one of its members does. Once one family member determines that he sympathizes with homosexuality or immorality then the rest of the family fears to offend him. Then they follow the usual pattern to first pity, then endure, then embrace.
A home that puts Christ first and defines themselves by their church callings and church service is not really putting Christ first, for they have rejected the foundation. The church exists to support the families, not the other way around. God is a Father, not a president, not a bishop, not group leader or a quorum president. This sort of family claims to be about following Christ, but they are more about showmanship, for they miss the spirit of the whole thing. They prefer to have the uppermost seats than to take the joy God intended for them in their families.
A home that puts Christ first, and recognizes that to do so almost always means family comes first is a home that is following the Savior in truth. Putting Christ first in truth requires knowing something of who he is. And Christ is a father and husband.
Christ began his recorded ministry when he was well into his adult years. He was no homeless vagrant. He had a family with Mary and Martha.
Christ put the Father before his own family, for when the Father sent him abroad to teach, he went and spent three years preaching the gospel.
Christ lived the principle that his home was a home centered on his Father first. He lived the same principle that he taught:
Matthew 10:37 He that loveth father or mother more than me is not worthy of me: and he that loveth son or daughter more than me is not worthy of me.
Christ did not love his mother, son, daughter, or wife more than he loved God.
But putting God first meant being extremely devoted to his own home. As far as we can tell, even being the Son of God, his ministry did not begin until he was well into his adult years. It seems that following the Father kept him at home.
Christ put his Father first. We see an interesting manifestation of that at the resurrection. Christ’s resurrection is known first to his wives, Mary and Martha. They not only know of his resurrection before even the twelve, but, rather astonishingly, Christ appears to Mary personally before he even ascends to his Father. Yet there were bounds. The Savior told Mary to hold him not, for he had not yet ascended to his Father.
And we need to realize that is all perfectly within putting the Father first. Christ appeared to Mary first because that was what the Father saw fit. But he would not allow Mary to hold him, again because he put his Father first. Christ put his Father first, which meant that he was peculiarly devoted to his family. He had the most important mission in the world to fulfill, but apparently spent many more years being a husband and father (likely around 11 years given a typical marrying age of 19 for men at the time) than he spent fulfilling that mission (apparently around 3 years). But he did so because he knew his Father well enough to know and obey his Father’s will.