Well, since we kind of have our own 'home-church' since we lost our last church (I should post that story here sometime, actually) here's a general idea of what we do and why.
Liturgy (order of worship) is a fairly flexible thing, and with a family church meeting it becomes more flexible because scheduled are more flexible.
I suppose the core elements are study (doctrine), worship, and communion. A lot of people would include group prayer on that list, and its good if you like that kind of thing, but to me that's not really what prayer is about. I wouldn't put community prayer as a core or central thing, I'd emphasis the need for 'closet prayer' and 'prepetual prayer'.
I'm very strongly opposed to modern didactics in a church setting. That is I'm against the model of one person talking and everyone listening, then its done. That is somewhat appropriate when dealing with new Christians who know very little about scripture, but with established believers (even kids raised in a Christian home who know the basics) I take a dialectic approach.
We generally take a book of scripture, I read it section by section (not verse by verse or topic by topic, but varying amounts depending on how much commentary is needed), give a general statement on its meaning and application, and asks if she understands it and what she thinks of it. In a multi-person (such as with kids) environment I pick someone depending on who has said the least and who appears to have the most to say on that particular topic. The discussion is often very brief, everyone agrees with what it means and we move to the next section. Even in that case its important that someone re-tells the passage in their own words as it shows they understood it and will remember it. Other times the discussion goes on and branches into discussing the history of the passage, how people use or misuse it and why, discussion on various ways it can be interpreted and which is most likely, and sometimes there are even disagreements that need to be worked through. That can take quite a long time but is well worth it, and since we're not bound to a 'lesson plan' or a deadline we can go through things like that.
We also do topic studies if something comes up. A few weeks ago I was discussing the meaning of 'women saved through childbearing' at the end of Timothy chapter 2, I mentioned it to her and she said she didn't know the details of that verse, so our next bible study covered Timothy Chapters 1 and 2, and we discussed it in detail.
We tend not to do as much with the kids under 5, though we do include our 6 year old from time to time, though she mostly listens. I probably should do some lessons designed for her though.
Time runs anywhere from half an hour to three hours depending how engrossed in the discussion we get.
We usually do worship related things at a different time or day than this. And worship can be anything from an acapella hymnsing to playing music and dancing.
Communion is very important, some people have made a very good case for doing it daily. I'd recommend it as a family on a regular basis.
As to how to get people interested. What does Mr. Frog study and what are his interests? If he plays his strengths and sees people listening to him he'll probably be fairly inclined to teach more. In a similar way if you find out what your teens don't know and want to find out you can grab their interest in this kind of meeting. Part of it is about meeting needs, a father needs to teach and kids have things they want to know about. If you can get that happening fairly regularly and everyone feels they are involved it could become something very grand.
