CO2, and other so-called greenhouse gases, does not heat the atmosphere but slow the rate of cooling.
CO2 cannot reduce the rate of cooling. It is incapable of it. It is not an insulator. It does absorb infrared light, but this is just another way for the surface to cool itself as it heats the air. It cannot in turn heat the surface again. You ARE violating the 2nd law of thermodynamics.
This is far more akin to a blanket than a greenhouse.
Both blankets and greenhouses work by reducing heat. In the case of the blanket, it does not keep a rock or a dead body warm. The only reason YOU feel warm is because YOU are generating energy under that blanket. Blankets reduce heat. That means you are not losing as much thermal energy as you usually do in open air. You temperature does NOT increase. You are warm blooded. Your body temperature is still the same under the blanket. You just don't have to work so hard to maintain it.
Actual greenhouses work by reducing heat, specifically convective heat. The still allow infrared light in from the Sun, which heats the interior, but heating of the outside atmosphere is reduced. The greenhouse will reach a certain temperature and then stop. It doesn't continue to get hotter and hotter. Why does it stop? Radiant heat is NOT stopped by the greenhouse glass. There reaches a point where radiant heat out (plus other losses) is equal to the radiant heat coming in. In open air, CO2 and any other 'greenhouse gas' do NOT reduce heat. They are part of conductive, convective, and radiant heating.
You are effectively trying to say that CO2 stops infrared light by absorbing it, and that this in turn increases temperatures of the Earth. This means you are reducing the radiance of Earth while at the same time trying to increase its temperature. According to the Stefan-Boltzmann law this is not possible. You are denying yet another theory of science.
It does not violate the second law of thermodynamics.
It does, and it also violates the Stefan-Boltzmann law, which I've just demonstrated.
CO2 has absolute ZERO effect on warming the Earth from the emitted light from Earth's surface. Zero, zilch, nada. No gas or vapor has the capability to warm the Earth's using infrared light emitted from Earth's surface. Absorption by any gas or vapor of surface infrared light does NOT heat the surface. Heating the surface is the ONLY way to make it warmer. You cannot heat that surface by using a colder gas in the atmosphere. You can't do it by conduction, by convection, or by radiance.
You can't do it.