http://www.moga.mo.gov/statutes/C500-599/5710000030.HTM
Carrying a weapon while intoxicated in Missouri is a Class D felony if the weapon is loaded and in functioning condition. If unloaded it’s a Class A misdemeanor. Only exception is if the weapon is being used in a defensive act.
Section 571.030.1.5
Permit or not it is barred.
Now... Will the law be applied to her or is she unassailable due to her political office and race?
Kind of a Catch-22. They can't charge her with carrying while intoxicated because they can't prove she was drunk. They can't prove she was drunk because she wouldn't take a breathalyzer test. She wasn't required to take a breathalyzer because she wasn't driving.