The concept of plurality within God is a denial of monotheism. The act of ascribing partners to God, whether they be sons, daughters, or other partners, is considered to be blasphemous in Islam. The Qur'an repeatedly and firmly asserts God's absolute oneness, thus ruling out the possibility of another being sharing his sovereignty or nature.
For his divinity, to put it in the simplest way:
Jesus was a mortal man. He was a man who was born.
God is not human. It also goes against this verse:
"Say, He is God, the One and Only;
God, the Eternal, Absolute;
He does not beget, nor is He begotten;
And there is none comparable to Him."
@Richard:
The fact that Jesus is seen to be God incarnate *is* what we deny. It is not only us. Jewish people also share the same view as us. To us, God is not a human man who walked the earth then killed himself to "save" humanity. We do not believe in original sin nor human sacrifice.