Do you have child safety locks enabled on the back doors? I'd check that first, then make sure you have the car set up to unlock ALL doors. Look in your owners manual for how to fix all the problems you've described in your original post. For a 2014 Cruze (not sure what year yours is) it starts on page 2-1 of your owners manual. It should be a pretty easy fix.
I would have sworn that I had actual mechanical child safety locks on the rear doors of my 2012 Eco ... Then again, I go through vehicles so fast, I could have it confused with another vehicle I owned at some point in the last 10 years ... LOL
My 2012 has a LED on the door buttons that lights up anytime the rear door locks are set in child mode. Also, there is a setting the infotainment system that unlocks just the driver door or all doors on the first remote unlock. The next time this happens check the front passenger door and see if it's locked or unlocked. If it's locked look through the infotainment system's controls for the door setting. If it's unlocked then check for the child lock LED on the driver door lock controls.
Page 27 of owners manual:
Keyless Access Operation The Keyless Access system allows for the doors and trunk to be locked and unlocked without pressing the RKE transmitter button. The RKE transmitter must be within 1m (3 ft) of the door being opened. If the vehicle has this feature, there will be a button on the outside door handles. Keyless Access can be programmed to unlock all doors on the first lock/unlock press from the driver door.
or page 125
Auto Door Unlock This allows selection of which doors will automatically unlock when the vehicle is shifted into P(Park) with an automatic transmission or when the key is removed from the ignition with a manual transmission with keyed ignition or when the vehicle is turned off with a manual transmission with pushbutton start.