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I would encourage her to get her CHL.
If for no other reason than to go to the class, hopefully with a good instructor, to learn the laws that you have to abide by, when you are with her and why you don't go to certain locations.

For your issue of her misplacing things - My wife loses her keys, shoes and phone in our house every day, as she will never put them in the same place twice.
However, for a gun, she leaves it in her car, and never has purse or on-body carried.
However I would not have any apprehension for her to on-body or in-purse carry, as it would strictly stay in her purse, and I wouldn't think she would ever remove it, unless necessary for defense.