Friend, you have errored greatly. Not all who believe in the bible have fallen into that doctrine.
Two, God is not something someone pictures in his mind. SO whoever told you that lie about someone having a picture of the Father in their head is lying. And if you believe we have a description of how God looks, you have been decieved b/c we who believe the scriptures do not.
As for the trinity doctrine, I agree with you that it's not true.
It's quite simple, if God the Father is not God the SOn, then they are two Gods, and if the Spirit is not the Father or Son, then you have a third separtate entity. Our God is One and not three. If you wish to understand the relation b/w the three, they are manifestations of God. God is made manifest by His Word (Son), He is manifested by the creation (Father/Creator of all life). Just as Adam is considered the father of us. And his Spirit that each person has in them. They are three ways that God is manifested.
Yahshua is considered the Word made flesh/Son of God. Because as even you Muslims admit, He did not sin, but lived God's perfect word to completion. He was one with it. Now, you say that God does not beget children in Islam as I understand (I could be wrong on your views). Yet, scripture says, what is born of flesh is flesh and what is born of spirit is spirit. God did not beget flesh but the Spirit that was in Him which is His Word (Son). He spoke and gave birth to His Word. I hope you understand this concept of Father, Son, and Spirit in its proper meaning.
Peace be to you friend...