"Family Integrated Worship" is an approach to Christianity and the church which emphasizes the centrality of the family, especially the parents' roles in the spiritual formation of their children. As I have written on a couple of other occasions on this topic, one aspect of family integrated worship is that the family attends the worship gathering of the local church together. The backbone of this family-styled worship, though, is located behind the closed doors of each individual family, which is one of the reasons I believe there is so great a hesitation among many to embrace family integrated worship as at least a viable alternative to age-segregated church.
Problem 1A: Men
Men struggle to be spiritual leaders. One of the main thrusts of Promise Keepers in its heyday was urging men to step up as leaders and fight against their natural (and often sinful) passivity. It seems that numerous books exist on the topic of being a "better" Christian man/father/husband. There's nothing wrong with striving for such things, but the real point of the issue would seem to be found at the obvious center: a knowledge of God.
Being a true spiritual leader in the home is not merely natural. A man cannot lead and teach in things for which he has no depth of understanding - and here's where I think many flee from spiritual leadership. It is easier (unfortunately) in many local churches to be a recognized leader in the church than it is to be a true spiritual leader in the home. Men who know their spiritual limitations (and we all have limitations) are often inclined to shy away from being discovered. For instance, a man who is not comfortable with his knowledge of the Bible may run from biblical conversations in order to keep from being found out. However, a man can serve on a church council and help make spiritual decisions without directly showing his theology (or lack thereof.) However, in the home a man cannot pretend with his wife and kids to be something he is not.
The kind of involvement in the spiritual lives of one's children which a family integrated approach calls for can be overwhelming. Personally, I know it is certainly not easy to spend time in God's word daily, let alone to call one's family together for even a few moments. (Hey, I'm a fairly new father - I know I don't have all the answers.) A growing spiritual life is really the starting place for us all - one does not need a degree in theology.
I often recommend J. I. Packer's book Knowing God because I think it is simply the strongest and most thorough book dealing with the matters at hand. I would rather a man read Knowing God than 10 men's books from the Christian bookstore, because ultimately the source of real leadership is that of an overflow of the heart of the man. Even still, Packer's book is just a summary of what a man should be constantly gleaning from the pages of Scripture.
Finally, I really appreciate the advice of a former pastor of mine who encouraged us to keep our family devotionals reasonable. With much grace he advised us to set our expectations small and not beat ourselves up if everything did not always work out. Sound advice, I believe.