Cant you get a device that wires into the ignition? you have to blow into it or it wont start, if it was me I would also get a cam and tell her. Certainly talk to her about what you have heard.
Forget trust and all the nicey nicey stuff. Its your car! She kills someone or herself (not nice if its her but thats the risk you take when your stupid) then its down to you pure and simple. Best way to look at it is decide now what your going to say to her friends mums or whoever she kills if she hits someone while drunk, 'i am really sorry but I didnt want to destroy the trust we had'?
'Sorry you kid died but I just didnt have the heart to take the car away until she could be sensible'?
I might sound harsh but then again the above is the reality, not everyone who drinks and drives kills someone, but every one who does kills through drink could of been prevented!
One last perspective.................
Do you ever tell your daughter not to get into a car with a driver thats been drinking? What would you say to a mother of a driver that killed your daughter while drunk, when she came knocking to your door? " thats Ok kids will be kids"? " yes its very sad your daughter killed mine, but lets face it we all have a drink and drive"??
You dont know me and I am sure you think I am horrible, but I am 15 and cant drive for two years. I have 2 friends that are old enough to drive, one I wont even get in his car!! He dosnt drink and drive but he is an accident looking for somewhere to happen and I dont want to be there.
Oh and tell her if you get the slightest hint she is drink driving or whatever you will call the cops, lets face it her not talking to you for a while is way better than you never being able to talk to her again

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Its not tough love, its sense and your meant to do whatever it takes to protect her, more than that you have no right to let her near your car if you even suspect she is doing something that might kill someone else..
Ok I am back to being nice again