However, we were in the facility (dealing with a so called mice problem by them) a couple days prior and noticed that they had cigarette butts in their rooms in huge ash trays and all smoke detectors had been removed and obviously it smelled like smoke.  

., and the only reason they are broke is because they blow all of their money at the casinos, and on cigarettes and going out to eat or to the bars, etc.If you go ahead and raise her rent to market rent, she will cope.  

I can tell you no smoking weed/or cigarettes allowed in my 2 rentals and if so they can hit the road.

And we all know how cigarette smoke clings to everything, including the smoker, so certainly the apartment's smell is not evidence of smoking.I don't want my tenants smoking in my building, but I'm not sure that such a restriction is enforceable.

I even had criteria that would get a tenant denied like: rude behavior, came with rude friends, showed up late without calling, missed an appointment, didn't fill out application completely after being asked to do so up front, smelled like cigarette smoke, had filthy car, just on and on. 

But during my inspection and walking of the place prior to close I can smell the strong odor of cigarettes and have seen the ashtray in his apartment.  

But, you'd be amazed at how someone supposedly broke finds money for new cars and cigarettes and the casino, etc.  

We don't smoke cigarettes. 

I had a Section 8 tenant who smoked something in the bedroom (whether it was marijuana, cigarettes or something else, I don't know) and two of the walls had what looked to be watery light-colored tar running down the wall and so smoking does cause damage. 

Again whatever you feel comfortable with in terms of escalation here.No personal experience with this device and not sponsored, but I've looked into FreshAir Sensor previously for my Airbnb, and it is a simple plug and play device that detects cigarette smoke.