You're paying her very much on the low end, and as pointed out, illegally underpaying her for overnight work.
If you routinely have her stay overnight, and you provide a spare room, then don't whine about toothpaste or food. But if she is de facto a live-in nanny then you need to restructure her salary. If you expect the same sort of hours from a future nanny (I assume you are going to fire this one) then you will need to sit down and think about adequate compensation.
...essentially just be in the house with DC
You are paying for her time, not for specifically what she does unless you have babies or small children who need to be occupied. You are also paying for peace of mind and your DCs' safety. As pointed out, security guards are paid for time, not by number of intruders they nab.
You will get what you pay for in terms of professionalism and you will get what you give in terms of your own professional demeanour too. Expecting top class service while lowballing someone both personally and in terms of money won't work.
You don't know who is buying her clothes. You don't know who is taking her out for entertainment. You should not be noting these details about her. None of this is any business of yours. Your job is to fulfill your legal obligations wrt pay and terms.
Oh and a nanny can get drunk in her own time, and can decide if she is in a fit state to supervise children afterwards, or drive to the job, etc. Just as you can call in sick, so can she. You can't expect someone to take the veil in order to accommodate you.