Improving appearance and odour are superficial things, underneath the teacher is still drunk and therefore should not be teaching.

Anybody turning up drunk to class warrants instant dismissal in my book. They can smell of rose petals and candyfloss for all I care, their smell is not the problem, their intoxication is.

Turnoi, you said that:

other teachers have a private life, and they should be allowed to do what they want in their free time as long as it is legal and has no negative impacts on his school work,

Does turning up to class hungover or still drunk (with or without a shower and breath mints), or finding such conduct acceptable, not constitute a negative impact on his school work?

Surely you can't think somebody either drunk or hungover is going to be able to deliver the same quality of lesson as somebody sober and well rested?

I understand you not wanting to lose an ally, especially one you have apparently just got back, but I'm afraid somebody with his views about women and worse his views about acceptable states for a teacher to be in whilst in charge of students make him.a rather worthless ally to have. You cannot say he is a good teacher when he admits to finding being drunk in class and doing the bare minimum for his classes acceptable.