Also, Michael sent Fredo to Vegas to run things. That was perfect opportunity for Fredo to step up and show he could handle the business. Michael saw how Fredo was moving and knew he was a weakness. Fredo proved Michael was right. Besides if you let Fredo slide others might feel they will get a second chance too. Blood relationships don't matter when it comes to Cosa Nostra. It's always business.
Michael did the right thing.