I keep a J frame in my car, but I never have kids in it. Personally, I would never use one of those key locks. The one time she forgets to unlock it, or relock it, will be the time it bites her. Also, even when locked, the kids can still open the cylinder and take the rounds out, which is something kids might do. I would not want a busy mom to try to have the discipline to make sure all is well every single time. Moms have a LOT to think about.
I would go with the lock off all the time and the gun in a small gun safe. It could be a push button or a key lock that is on a quick-detach from her key ring. That way she doesn't have to depend on a habit pattern.
Heck, I can't get my wife to remember to set the alarm on the house all the time when she leaves and she doesn't have kids to worry about anymore!
Then there is the old joke:
"I got a J Frame for my wife."
"Good trade!"
Badumpbump.