In order to safely secure doors for the safety of your mother, you will have to get a lock smith to install a lock that can only be opened with
a key from the inside.
The caregiver or caregivers must each have a key. Also, you need to have one hidden inside the house so that each person in the house knows about it, except your mother.
You will need to train each person to react quickly to unlock the door in case of fire or other emergency.
Also, there is a good chance that your mother will be angry about not being able to get out. She will probably look for the key obcessively. So you need to train yourself and your caregivers about how to deal with her anger. You may have to say, "I am sorry mother, but we have to keep you safe." You may have to say it over and over.
In my experience, it is necessary to safely secure the doors, especially at night. Other wise there is a very good chance of the elder getting out at night to wander. The only other alternative is to have a caregiver sitting up all night, which is very expensive. The locksmith may cost a fair amount, but it is not costly if you think of the alternative.