Rear A/C blowing hot air

This could be a number of things but the most likely cause is the rear blend door is not operating.

Here is a guide on how to replace a front actuator so that it will help with some info but clearly this is going to be in the rear for you:

https://www.2carpros.com/articles/replace-blend-door-motor

Below you will find the process from the manual on how to replace this and perform a calibration.

This is assuming that the front is operating properly at proper temps. There is a chance that the system being weak can cause the front to work for a short time after the rear stops. If you want to, you can check the pressures just to be sure the system is not low.

Here is a guide that will help with this:

https://www.2carpros.com/articles/re-charge-an-air-conditioner-system

Please run through this info and let us know if you have other questions. Thanks