If everything has a purpose then evil doesn't exist

[R-Farmer]

So what you are saying Yahweh was never by itself

Not till the cross. Which is why Jesus cries out ' My God why have you forsaken me' Or Why have you turn your back on/left me?

 Does the son spirit have independent thoughts?

I'm trying to think of one example, but I can't come up with one where Jesus wanted to do X and the Spirit Y.

How about the spirit?

Does the Father and Jesus have independent thoughts? yes. The night before Jesus was to be captured tortured and nailed to the cross he went to the garden at gethsemane and prayed to God so hard his sweat turned to blood, asking that if God would find another way than the cross.  

 Can either say no to Yahweh ?

Apparently Jesus could have in the garden, or again when He was tempted by satan. (satan offered to make Christ ruler of this world without having to go to the cross if Christ would just kneel to satan.