The portrayal of Mike’s relationship with Tom is very complex.
There’s no mention of any fights between them in childhood, unlike with Mike’s blood brothers. But we must remember that they were the most educated, intelligent and cool people in the family. They didn’t need to have things out in that way. Tom was the closest person to Vito, admired him and learned a lot from him, we may say that Vito’s influence was a decisive factor for his personality. Mike, in turn, was a “reincarnation of the Don himself”, and as such was groomed by Vito and Tom together. Being his teacher, Tom was very impressed with Mike’s talents in “business”, and there’s no doubt that Mike always had great respect for Tom.
They had a lot in common; in fact, they had more in common than Mike had with his blood brothers. They learned a lot from Vito and admired him. They were very smart and manipulative, penetrative and patient. Mike had more Sicilian cunning, but they both had brains and breeding enough to act in businesslike manner where business was concerned, and not to allow any hostility between them.
In the beginning we read that Tom always liked Mike. But there’s also such a quote: “He (Tom) had never thought of her (Mama) as his mother as he thought of the Don as his father and Sonny as his brother. His affection for her was like his affection for Freddie and Michael and Connie. The affection for someone who has been kind but not loving.”
So we conclude that despite the fact that they were never close as brothers, Mike was always kind to Tom, and they respected each other. Of course Mike would never repeat Sonny’s mistake in underestimating Tom’s opinion. And never could he be so primitive as to insult Tom for no reason – that’s just stupid for Mike, how could FFC screw both great characters in such ungifted way!
And one more thing. When Mike moves Tom out of the action it’s not personal. He has other reasons. All this situation is analyzed in this thread: Why keep Tom out?
At the first opportunity he returns Tom as the consigliere, and Tom is the only person he needs and trusts at the most difficult and dangerous moment in his life. And even though Tom cannot be treated as an equal by Don Michael, when he asks Tom not to give stupid advises, it’s stated that “ for the first time he was cold with Hagen”.
And no one else but Tom is dispatched to bring his wife and kids back. The mission he’s trusted with speaks for Michael’s opinion of him.