Welcome to the forum. Haynes & Chiltons are very poor manuals as far as giving any real depth. They can be wrong, misleading & useless for this type of repair.
The factory 200/Avenger (JS-body) service manual is much more accurate & detailed.
The factory service manual is copyrighted with TechAuthority as the sole authorized Chrysler publication distributor. Look for a used copy on ebay?
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Think of it as a tool cost. It could pay for itself, especially if you do your own work.
The left/right temperature difference could be from a partially clogging heater core. Chrysler allows a 12º difference between sides (it is mostly much less than that).
Usually at the start of the cold season we get some posts about heater and thermostat issues, The 'Search Community' at the top of this page will show you past posts from others with whatever you type in & search for.
Door actuators usually make clicking noises as they fail. Don't jump at an actuator first without some diagnosis.
If this HVAC is a single-zone temperature control, it probably isn't the blend actuator at fault.
Has the car cooling system been maintained? At 10 years old, it is due for a flush. 2012 may have been the last year that Chrysler used HOAT coolant. Use distilled or very soft water for the fill. Make sure that the coolant you use says that it meets Chrysler MS-9769.
You might consider a 'power back-flush' to force any loose corrosion out of the heater core.
The HVAC control can be accessed with a capable scan tool for door re-calibration & display related fault codes (not OBD2 codes).
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Thanks for the great info .. My daughter just tiold me that when the problem first began, she heard a clicking noise , I hiope it;'s just an actuator ..
