You don't know what you're talking about.
What happens is that incoming solar radiation impinges upon the atmosphere.
It it not monochromatic.
Different molecules in the atmosphere absorb a portion of the solar radiation, according to (for example) their vibrotational modes: jumping between such and such vibrational-rotational level, to a higher level, requires energy of some amount.
Incoming photons corresponding to that amount of energy are absorbed by the molecules.
The molecules *may* radiate the energy latter, but not necessarily going to their original state: perhaps they release a smaller amount of energy; perhaps they collide with another molecule undergoing inelastic transitions; so on, and so forth.
The idea behind "global warming" is that CO2 preferentially absorbs energy in the IR band, and the re-release of this energy warms the planet. The analogy is made to a "Greenhouse".
But there are a number of flaws with this.
One of them ... if you dig for it, is that a greenhouse does not attain its temperatures because all of the solar radiation is absorbed, but because it is *enclosed*. The air is trapped: and being in an enclosed space there are heat transport mechanisms which are not active, which are seen in the big wide world.
Another one, is that the absorption of CO2 is what is known as "saturated": this does NOT imply, as you took it, that the atmospherre holds all the CO2 that it can hold, but rather, the CO2 which *already exists* (in addition to water vapor, btw, should you care to look it up), absorbs basically ALL of the incoming IR band light from the sun.
In other words, adding additional CO2 will not increase the heat absorbed by the atmosphere.
(Think of it this way, in another connection. Let's pretend ISIS or Iran has detonated a small nuke in San Francisco, and you're across the bay in Oakland. You want shielding to protect you from fallout. Let's say your back-of-the-envelope calculation has told you that a three-inch sheet of lead will absorb all of the radiation. At that point, adding another six inches, or even a foot, of additional lead won't absorb any more radiation: all the radiation that came at you is already absorbed by the first three inches of lead.
And so with solar radiation. If the existing CO2 already gobbles up all the incoming IR from the sun, adding more CO2 won't cause any more to be absorbed: it may (depending on the concentration-altitude distribution of CO2 -- and that depends on temperatures, and plant cover, and reflectivity of the earth's surface, and whether you are above land or ocean, and the solubility of CO2 in water, and therefore the temperature of the water...) )
There are a couple of other problems with the models; among them being predicted feedback from changes in CO2, or moisture; the fact that the models are not matching the actual recorded data very well, either qualitatively or quantitatively; poor stewardship/maintenance of the data (e.g. the "hockey stick" and the "hide the decline" emails from East Anglia; the refusal to release some raw data sets to third parties (a scientist refusing to divulge the raw data is ALWAYS a red flag); failure to note that CO2-temperature correlations from the past show CO2 increases as LAGGING the temperature increases, instead of preceding them...
And, as always, follow the money and power trail.
Hint: China has been building one or two coal-fired power plants for YEARS. India likewise has been adding fossil fuel capabilities. Each of their economies (in terms of CO2 emitted per unit of economic output) is far more inefficient than the US; so that the US going back to 1950s levels of pollution will not make up for the increase in Cow by China and India: yet they seem to be curiously exempt from the restrictions. And the number of Democrat donors and cronies who have grown wealthy off of this, even while their companies either go bankrupt (Solyndra) or cause other unforeseen ecological disasters (bird strikes on wind turbines), is very instructive.
If the "no fossil fuel crowd" were intellectually honest, they'd be pushing nuclear power (France gets 70% of its electricity from nuclear power). But that was discouraged years ago on orders from the Kremlin, as a back-door way to try to attack the US nuclear weapons capability. Even with that, however, there are more promising forms of nuclear reactors (pebble bed and molten salt reactors, thorium reactors) which don't have the risks of the Cold War era reactors. How come those are never considered or pushed?