To what extent does the Son submit to the Father? How does that relate to marriage roles?

There is voluntary subordination, a voluntary humbling (which is also what we are told Jesus did), where the ‘subordinate’ chooses to obey.
 
And I think this puts the question of Jesus’ motivation to rest:

Let us fix our eyes on Jesus, the author and perfecter of our faith, who for the joy set before Him endured the cross, scorning its shame, and sat down at the right hand of the throne of God.
 
Hebrews 12:2

 
That is the reason God created in the first place, to increase his joy.