Police, Race, and Federalism

As people around the world continue to protest police brutality, Republicans and Democrats in Congress have proposed bills that would reform policing across the U.S. But in the American system, states are given a lot of latitude over law enforcement, down to the use of tactics like chokeholds and tear gas. Given the constitution, what can the federal government actually do to make things better? Also, why was the ever-obscure Third Amendment trending last month?