I have a similar situation, except it's an ex-husband and my daughter is 12. Last month he came to her after-school care very drunk and tried to take her out and drive her home. She wants to see her dad, I want her to be safe.
So on one front I am working towards gaining sole legal custody. In the interim, these are the rules for visiting:
1. She doesn't get in a car with him. I drive her to/pick her up from wherever the visit is happening (usually his place).
2. Visits are short (2 hours) and scheduled by me.
One important thing where I would disagree with some of the previous posters - I would stay away from anything that involves monitoring his sobriety. You've mentioned breathalyzers and his own self-report, both of which are causing problems (he lies about self-report and he complains, interferes and obstructs with mandatory breathalyzers). Someone told me once "it's not your job to catch him drinking, it's his job to prove to you that he can be trusted to stay sober".
If you've had a long enough run of him being dishonest or making excuses for his drinking, maybe you should consider setting your default to "he's drinking unless he proves otherwise", and release yourself from the burden of having to ascertain whether he's been using alcohol or not in the recent past.
How does he show that he's consistently sober? It's up to him to do it. If he's in a 12-step group, does he have a sponsor who will get in touch with you? Does he have medical professionals who he can authorize to talk to you? Has he had a good long run of time (six months or a year) during which no alcohol-related incidents have happened and he has been completely reliable? What would you accept as evidence that he is sober and reliable, that doesn't put you in a position of monitoring and checking up constantly?
With my ex, I'm trying to put the burden of proof on him. If he wants longer visits with Kid, he needs to be pro-active about his alcoholism and not just tell me that I can ask him to use a breathalyzer or I can check his apartment for bottles.