Who represents the government in these cases?

Generally speaking, the way it's supposed to work is the local prosecutors will start the process. That, unfortunately, isn't something they like to do because they have to work with police departments. If they fail to do their job, theoretically the next step is that the FBI gets involved. But, doesn't seem like today's FBI is doing much beyond prosecuting Trump's political enemies.

This is the reason why I've long believed we need a check both federal and local to police that is completely divorced from regular prosecution. We need lawyers/investigators whose sole purpose is investigating and prosecuting police at pretty much all levels of the government. The federal government theoretically has that with the office of inspectors general.

The government prosecutes the government and is judged by the government and a jury screened under voir dire by two government lawyers?

Kind of like when a robber comes to your house, you have him arrested, and when you go to court you look up and he is the one swinging the gavel.

Of course, interesting the cop has to know there is a constitution violation. Somehow ignorance of the law is always an excuse for the cops but the citizenry must know all 190,000 pages of federal regulations and 300,000+ laws and by god if they forgot one they are fucked.