You left out "in His humanity." That is crucial. God accomplishes things with one divine will, not three wills. Christ, on the other hand, has a divine will which is the same as the Father's, and a human will, which is in perfect obedience
The Athanasian Creed spells it out clearly as well: "Equal to the Father, as touching his Godhead; and inferior to the Father, as touching his Manhood." That is: inferior only in His humanity.
You did not differentiate. You simply stated the Son "does as the Father wishes." That statement is one of subordination, and obedience. There is no difference between the will of the Father (Wisdom) and the Logos (Word) and the Spirit of God. They are of one will, and one nature.
[formatting caused the last part to be dropped when I posted]
Doing as the Father wishes does not imply that there is any difference in will. It is a matter of order. Just as the Spirit testifies of the Son. This doesn't indicate that the Spirit is inferior in any way to the Father or Son. It is just His role. Jesus will return as King of kings and Lord of lords to get His bride, the Church, at a time the Father determines. Again, there is no difference in will here. Just a difference in operation. Each member of the Trinity has a certain operation which is a unified outpouring of their will as the one God. The Spirit is doing His work in the life of believers and points to the Son. The Son addresses people to the Father. It is an order, not a suborder. And, yes, their divine will is exactly the same.
As a side note, it is interesting how the Second Coming of Christ paralels the Jewish wedding ceremony. A groom is espoused to the bride and goes away for a time to prepare a place for her with the promise that He will come again. When the father determines the time is right, the groom then returns for His bride.