I believe Jesus has the will of God and the will of the physical body. So the Spirit of God in Jesus has an indistinguishable will from the Father's will.
The Paraclete has the will of God and the will of the person who has invited Jesus to be Lord and Savior.
There are three persons due to the fact that God is modified somewhat by the bodies He inhabits or doesn't inhabit not that God has changed but rather that the bodies modify what God can do.
Do I correctly understand that you mean God is one entity who has three manifestations? If so, I agree that this makes sense, is a workable model of Threeness.
Unfortunately it's not what the Trinity Doctrine says. It says that each of the three persons is simultaneously that person and 100% of God.
And as I mentioned it also says that the Trinity Doctrine is incoherent, whereas the model you propose is coherent. As I said above, the churches hold that the Trinity is "a mystery in the strict sense". And when you look that up, you find it means "cannot be known by unaided human reason apart from revelation, nor cogently demonstrated by reason after it has been revealed" (Oxford Dictionary of the Christian Church, but a parallel definition can be pieced together from the Catholic Encyclopedia under "trinity" and "mystery" and "mystery in the strict sense").
This puts the Trinity in the weird position of having no sensible explanation, with the corollary that any sensible explanation is wrong.
So my question in this thread is, Does each of the three persons have [his] own will? ─ in which case there are three gods. Or do the three persons have only one will, in which case your explanation works well.
But having a proclaimed incoherence at the center of the concept is a rock on which any explanation might founder.
(And I repeat that in the NT, each of the five versions of Jesus, those of Paul, Mark, Matthew, Luke and John, says he's NOT GOD, and never once claims to be God, I can set out the quotes again if you wish. That is, the Trinity Doctrine is contradicted by the NT.
However, that doesn't stop anyone accepting the Trinity Doctrine, incoherence and all ─ it simply prevents the claim that it's supported by the bible.)