I’d be surprised if Frank Sheed said what you have quoted him saying. My guess is that you have misinterpreted his meaning. The Son has two natures and thus two wills, however, the divine will of the Father, The Son and The Holy Spirit are one.
Aquinas points to internal procession vs. external procession. The Son proceeds internally from The Father and the Holy Spirit proceeds internally from both.
Aquinas quotes Athanasius as being correct in his statement - “The Holy Ghost is from the Father and the Son, not made, nor begotten, but proceeding.”
Aquinas - “in God the act of understanding and His existence are the same”
Aquinas calls the Son the Intellect/Word of God and the Holy Ghost the Will/Love of God.
The Son, being God’s intellect is the full and supreme perfection of God.
Aquinas- “as the divine intelligence is the very supreme perfection of God, the divine Word is of necessity perfectly one with the source whence He proceeds, without any kind of diversity.”
Something to take into consideration - Aquinas uses the words God and Father simultaneously as is often the case in scripture.
I would suggest reading this whole section for further understanding newadvent.org/summa/1027.htm
Here is a link the