Different atmospheric models available for personal usage?
Unfortunately, I don't think such a numerical model exists that would be suitable for high school students' understanding. The simplest climate model around is a zero-dimensional (energy balance) climate model, but a background on mathematics, and programming may be necessary. You can find one here. Wikipedia has one listed. Michael Mann has the source code for such a model, but it is written in MATLAB (you may be able to run it in OCTAVE, since MATLAB is licensed). There are likely many more than just these, considering multiple layers, volcanic eruptions, etc.

The code for the models listed are simplified models that do not consider things like clouds, aerosols, eddy diffusion, etc. This is where Global Climate Models (GCMs) differ. They must consider how fine details, some of which aren't considered by weather models, affect the climate. Therefore, they are usually complicated. Most GCMs I have seen are written in FORTRAN, which is an antiquated language, but computationally efficient. This makes even easy concepts obtuse.

While I have not dealt specifically with CESM, I can infer some things about it. By definition, CESM is an earth systems model, not an exoplanet model. You may be able to adapt some of the parameters to other planets, but it becomes too difficult for just one person to do (because of FORTRAN). There are models for other places, such as GCMs for Mars, but they are difficult to run and not necessarily accurate. Clusters are needed due to memory limitations, and how long they run for.