Is it controlling to ask someone to stop drinking entirely?

Yes I voted YABU because it is controlling. You can't tell him to stop drinking. And it won't work, he has to decide for himself. My DH is an alcoholic and it was the hardest lesson for me to learn. I can't control him. I can only make my own choices and tell him how is drinking is affecting me. What I did feel was reasonable which borders on the edge of this was give up drinking myself and say I wouldn't have alcohol in the house. This was after a serious incident so he could agree his drinking was damaging, if your partner doesn't have this insight then he might not agree to it. Of course my DH didn't stick to it but it made the line clearer. Then I had to make my own choices, to live with an alcoholic or leave. You have to separate controlling him from making your own choices, you can only control your self.

It's fine to issue the ultimatum given your update, he's breaking the law and acting irresponsibly and dangerously when in charge of minors. These would be definite deal breakers for me in a relationship. You have to be prepared to follow through though and leave the relationship if he's refusing to give up alcohol completely.

Yeah. That’s rehab or divorce territory.

YANBU to ask but he Wnbu to say no if he’s not ready.
He needs to do it for himself and to want to do it.

Generally speaking I don't think asking a question is controlling if you accept no as an answer.

In this specific situation, I think it depends what "crossing the line" means to you. If he's just getting a bit drunk occasionally - yeah you're probably being OTT. If he's smashing the house up and calling you every name under the sun - not unreasonable at all.

However the danger now is that he will turn this into a power game with you as he’s clearly got little self reflection over his own drinking habits. I would be careful now of what you do next as any sign of attempting to “control” him as he’s framing it is now giving him the excuse to drink. A poll here isn’t going to help you persuade him you are right. Once a person has gone into the denial phase of drinking and then framing you as the problem for noticing, you will need to learn new techniques and tools in order to deal with him so he listens. But depending on how bad it is you may not be able to influence anything.
When you say crosses the line, what kind of things do you mean?

Not if they are a functioning alcoholic and their drinking is affecting other people or themselves. Give them the option to stop drinking or they leave

Is he an alcoholic?

Of course he thinks you're being controlling, he doesn't want to stop.

You can't make him stop drinking, but you can stop the relationship.