So she has a permit, she has been around guns but not shot this gun and you feel the need to take her gun from her? Is she mentally unstable? If so, why is she there to help with the kid, otherwise give her back her gun...
If some thug perpetrates a home invasion with your house as the selected site, you'll wish she had the gun.
p.s. There is no such thing as a "pistol permit." There are concealed handgun permits (some states use different terminology) that allows the permit holder to carry concealed (in purse, under a shirt or jacket, etc).
The OP's MIL has one, and had enough sense to bring it with her to Louisiana. I think she's way ahead of the OP in terms of family security. I don't think the OP, based on his comments ("have not owned a handgun in a very long time"
), is the best person to evaluate her competency.