I don't see the contradiction. What we mean by a "monopoly on violence" is that the government decides who and under what conditions gets to commit violence. The government orders soldiers to kill enemies. Law enforcement officers are allowed to use deadly force under certain conditions. And in the US, citizens are allowed to use deadly force under certain conditions.

The key issue is that government (via courts) is the one that decides whether violence is justified or not.

You're right that a government that no longer represents its people must be replaced. But that's not the case in America. The conflict in America is between two different groups of people with different ideas about what the right thing to do is. So far, these two groups have used democracy to get their way. As long as that continues, there is no problem.

But when people use violence outside government law, just because they don't agree with the decisions of the government, then that's not justice--that's just terrorism.