Are you open to another interpretation?
One manifestation of his spirit was separated by the veil which hid his true self. The will of the Son simply means the will of the carnal flesh. He submitted the flesh to his spirit. Two wills in one person.
I've read several spirit world books that show how we all leave a portion of our spirit in the spirit world when we incarnate. It might not be true, but there is eyewitness testimony for it being true.