If a hostile country has installed a puppet leader to dismantle your government from the inside, and violent revolution would only expedite your governemnts destruction, how do you combat it?
Why do you believe said government is worth saving? Is it particularly robust or advanced in some way? If it's the country that I'm assuming, your government is currently functioning exactly as it was designed, and the incoming administration is not the coup you seem to think it is.
The adversary gets a much, much more significant advantage from holding your government captive and using it to further their interests. If they wanted to simply remove it from play, their angle of attack would differ.
Their angle of attack is the only angle. If they ever had full control they would no longer be an adversary. Destroying the government holding them back would be to their every advantage and is their end goal.