How does the command to honor father and mother relate to God?

There is no doubt that God is there in that command. He is very powerful and dominant, and parents ought to want to demand respect for themselves for the long term preparation of their children to respect God.

I think the reason there is such a thing as parents is so that children will learn what it means to have God as a parent. And the reason there should be reverence and awe for a mom or a dad is so that a child will learn what reverence and awe for God is like.

So, yes, there is someone in the background of this command. It is God. It is Jesus Christ, and it is the Holy Spirit. A parent ought to have in mind from the beginning that the way they hold their child, spank them, affirm them, and demand things from them should be telling them, showing them, and giving them a feel for who God is, both in his sweet and tender side and in his tough, powerful, just, and wrathful side.

God is very much there in the background, and a child ought to see right through mom and dad eventually to God.