To answer your specific question, mouthwash is about 2/3 the alcohol content of hard liquor (Listerine is 27%, compared to whiskey or brandy at 40%). Vanilla extract is 36%, and is a really, really expensive way to get drunk.
Listerine also contains some other alcohol-like compounds (eucalptol and thymol) that may have toxicity issues of their own, and some other ingredients--all of which give the liver a workout and probably lead to one hell of a hangover (kind of like vermouth). But I think the toxicity of the ethanol is the important thing. From your description, she's basically drinking the equivalent of about a liter of bourbon a day.
It doesn't matter whether it's Listerine, single-malt whiskey, or Old Times. The fact that she's drinking whatever is in the house is the issue. She's got a compulsive drinking behavior that she can't control. I agree with Jon: do whatever it takes to break the behavior. And it sounds as though it would be safest if that were supervised. As you know, it's what happens after she's detoxed that will determine whether she achieves long-term sobriety.
Take care of yourself, and please keep posting.
Don S