Fredo had two primary problems: huge insecurity and frustration.
His behavior regarding Michael derives from those two. Yes, he may have resented his brother, but I don't think it extended to hatred or a desire to see him dead. I also don't think that Fredo was a strategic thinker. His vengeance (if any) was temporal; here and now.
It's all rather complicated when you start speculating about motivations. However, I am surprised that someone who had Michael's intelligence and intuition did not pick up on Fredo's feelings.