How to create a backup image (*.ab) of Android Device that is not booting up?
The approach you are taking is not worth it for you simply because: 


USB debugging needs to be enabled beforehand for using any adb command on a device. Since your mother probably would have never felt (and why would she anyway?) the need to enable it, assume it to be disabled. 
Since debugging can only be enabled either manually by the user under Settings app, or by using a custom kernel, or by using a custom recovery to make changes in data partition, your chances of enabling it are zero. 
Even if debugging is enabled the two most important processes are either not started or not fully functioning for enabling and approving backup via adb. One is the activity manager which is required to seek approval for backup via UI, and the other is the backend backup service which nobody can tell (without logs) whether it is started or not because of the boot issue.


In short, dump this approach because it is futile and a waste of time in your case. All I can suggest is to find out a way to either load a custom recovery somehow without deleting userdata. I've never tried that, so that's all I can offer.

You can try looking for Qualcomm chipset flashing type tools. They may be able to help you load a custom recovery/kernel so that userdata partition can be accessed.   Beware with such tools though. They sometimes don't list partitions for selective partition flashing and flash every partition in wholesale, including data partition which is of prime importance here. Good luck!