Conducting times of family worship is simultaneously one of the most fruitful and frustrating activities for a family with little ones, at least in my case. It's absolutely wonderful, but it can also be a "hot mess."
No doubt the frustration is all part of the process of growing in grace and humility. So, let me be clear to say that the goal of family worship is not monk-like tranquility and perfect order. However, one of our goals in family worship ought to be teaching our family basic Biblical truths that lead to clear understanding of the gospel. We need tools to keep us on track and provide structure.
One tool that has been useful to me is a catechism. I know it sounds stuffy, formal, and outdated. But, it's not. On the contrary, it's an effective and fun way to interact with children during family worship. It is also a method that has stood the test of time in the Christian tradition.
A catechism is simply a series of questions grouped in categories. The teacher asks the questions and the student answers. They are meant to build on each other and tell a story.
I have developed a short catechism that I use with my children that may be helpful to you. I used a chronological structure that follows the major epochs in redemptive history.
You can download it here.