In the Book of John, we read about Jesus promising His disciples the Holy Spirit, whom He refers to as the Advocate (John 14:16, 26; John 15:26; John 16:7). As simple as these verses may seem, they have actually caused a rift in church teachings: was the Holy Spirit sent from the Father and Son or just the Father? It might not seem like an important question to some, but there must be a careful answer to this question, so as not to cross the line of heresy.
If one were to say that the Father alone sent the Spirit, then what does that say about the Spirit and Son? To some, it may mean nothing. But others might interpret its meaning to be that the Spirit’s and Son’s deity is unequal with the Father. On the other hand, if one were to say that the Father and Son sent the Spirit, then may interpret that to mean the Father and Son are equal and the Spirit is unequal.
We should answer this with caution—there is still a mystery to the Trinity. A closer look at the verses in John regarding the sending of the Spirit (Advocate) tells us the Spirit was sent by the Father and the Son (John 15:26). But combined with other verses in John about Jesus, we see the Son was also sent by the Father. This indicates that the Spirit and the Son both came to us in obedience to the Father.
The Trinity works in unison, with each having a separate role. As we can see throughout the gospels, Jesus worked in submission to the will of the Father through the leading of the Spirit; and likewise the Spirit worked in submission to the will of the Father in leading Jesus.
So it seems the Father leads (appropriate for the role of a father) with the Spirit and Son both in obedience. This does not diminish the unity of the Godhead any more than an earthly son obeying his earthly father does not diminish the unity of a family (though we should not take this example literally like the LDS church). Perhaps the obedience of the Son and Spirit only helps strengthen the Trinity’s unity, as would an earthly son obeying his earthly father strengthens the unity of an earthly family.