Would suggest you talk to Al-anon as they can help family members of problem drinkers.
His drinking is impacting on your family life and it is thus a problem. It has become the elephant in the room because he keeps denying the extent of his problem. You are also becoming increasingly unhappy by the whole situation. I think your anxiety is caused by his drinking and the consequences that stem from that.
Your partner is likely too underestimating how much he is actually drinking weekly and this is impacting on your family life. He is not spending time with yourselves on the weekend, you also have to fetch back his car from the pub. The other thing that is worrying re him is his denial (he is saying that he is not dependent - I would actually argue he has become dependent. Denial is commonly seen in these situations too) and saying that he does not drink every day. You don't actually have to drink every day to be or to become alcohol dependent.
Has he ever tried to stop drinking and if so how long did that last?. My guess is he cannot give up drinking for any real period of time (what's the longest in your reckoning that he has gone without alcohol).
Was he drinking to this extent when you first met him?. If so did you think that once he got with you and had a child he would somehow "change"?. Am sorry to ask those but these are questions that you need to answer to your own self.
Many women in these situations end up as their partner's enabler - how many times have you made excuses for him and to your own self (not just your family) re his behaviour?. Likely more than once. And I reckon as well not many (if any) people know the full extent of his drinking problem.
You cannot and should not enable him - enabling will only give you a false sense of control. Enabling as well shields the person from the consequences of their actions.
If he leaves his car at the pub do not fetch it back for him!. Do not make excuses for him, no covering up for him as of now.
An ultimatum won't work unless you are prepared to see it through to the letter. Also you cannot keep issuing them.
This is also not just about you any more - there is also your DD to consider here too. She has no say. Children who grow up in a household where one of the parents is alcoholic/alcohol dependent can themselves go onto develop their own set of emotional problems as adults because of the drinking and are more likely to choose an alcoholic for a partner. You cannot leave her that potential legacy.
I realise you do love him but sometimes love is not enough. Love turns to hate very quickly and you may end up completely resenting him for what he has done.
You cannot save him or rescue him ultimately if he does not want to be helped - you can only save your own self and your DD here.
Do seek support for your own self and contact Al-anon. They are very helpful, I will put up their details for you.