I was involved for a while when I was in the AF, stationed in Indiana. Went to a couple local meeting with local representatives first responders and hospitals. Not very high in the hierarchy, but somewhat clued in.

We had exercises on the base, but also large-scale joint exercises that included several local hospitals, fire departments, police forces, press, and others I'm probably forgetting.

We planned extensively, but...
You know that saying that "No plan survives first contact with the enemy/reality"? Plans aren't supposed to. Plans exist so people have some idea what to do next. They make it possible to improvise. They main keys to that working are communication and trust. You can be the most bureaucratic bureaucrat in the world, but if people you supervise tell you something and you listen and understand and trust them, you can still succeed.

FEMA, the organization, ought to be facilitators/coordinators, and that's all. Spend most of the money on training and equipping the people who do the job on scene.