The relationship between Christ and the Father is simple: They are one in the same - as is the Holy Spirit.
ONE God in three persons, not three persons in one God. If you think Jesus did not exist until he was born of Mary, you may be confused by this. The Father, Jesus and the Holy Spirit have existed since the beginning of time When any of the three persons of the Godhead act, they all act.
So, in answer to “what do they think about each other”, they think what you think about yourself.
The Divine Jesus did not subject himself to the Father because he is the Father (none of the three persons Father, Son or Holy Spirit can argue with each other because they are not individual Gods). The Human Jesus subjected himself to the will of the Father out of love for worthless man.
Help any or did I just muddy it up?