Nope, it has nothing to do with trust at all. It has to do with Love.
God Loves you unconditionally, you don't have to do anything to earn that Love, it has already been given.
I agree with you statement "God loves us unconditionally".
Also, I believe God chooses to entrust some disciples with more revelation of himself than others, and trust is not the same as love.
I believe Jesus loved all the disciples, but at the same time, his father trusted Peter more than he trusted the others. The scripture supporting this premise that revelation is based on trust and relationship follows.
Matthew 16:15-19
15 He said to them, “But who do you say that I am?”
16 Simon Peter answered and said, “You are the Christ, the Son of the living God.”
17 Jesus answered and said to him, “Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven. 18 And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it. 19 And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed[d] in heaven (KJV).
My understanding of this passage is that Peter had been lifted up by means of the father revealing something about Jesus which was not revealed to any other man at that time. Jesus was surprised to know that Peter had been given this revaluation and after Jesus confirmed what his father revealed to Peter by blessing Peter with the purpose of establishing the first church.
To tie this back to the original thread, position in heaven will be based on relationship which will be confirmed by revaluation and the revelation will be tied to purpose.