I'm pretty certain state governors are the only ones who can deploy the National Guard.

Guard members can be nationalized, and I think the president could nationalize them for this. But it's insane to do so. Alabama desegregation is a great example. The Alabama governor deployed the Guard to stop desegregation, so the president nationalized the same troops to force it.

I'm also pretty certain that while they've been used for peacekeeping in the past, I'm pretty certain the National Guard doesn't have very in depth law enforcement training.

Oh god this. As a former member of the Army National Guard, they barely have army training. They're trained, and I'm proud of my service, but they need additional training before deploying anywhere for anything. The Cold War philosophy was the front line troops would slow the soviets down long enough to deploy the best regular Army units. The lower tier regular Army would follow in weeks, and the Guard would follow in months. Even when doing their primary jobs. Pretty much the only thing the Guard can do out the gate is fill sandbags for floods.