Tony's motivation wasn't just that kid's death (which was caused by Ultron, his creation btw) but also a desire to keep the Avengers together.
Rhodey's motivations were more a desire to acknowledge authority and order, not sure where you're getting fear from.
The Sokovia Accords wasn't about outlawing vigilantes, it was about sanctioning the Avengers. T'Challa didn't sign it and he's not a superhero. He doesn't even act as a vigilante in the movie, he's just a man on a revenge quest.
Tony didn't know Zemo's true goals until the very end, he along with everyone else thought he was after the other winter soldiers. The assassination of his parents was also never revealed to him, he believed they had died in a car accident. Tony going nuts at the end was also him at the end of his rope, when most everything he holds dear had been taken from him, and after the person he grew up listening stories about from his dad revealed he had betrayed him as a friend. There was a build up that you seemed to have missed that caused him to lose it.