Every person is a mixture of good and bad ... & you are better placed (than we are) to know whether ur DH's good points make up for his bad.
Personally I hate drivers who drink. I am a zero tolerance sort of person.
I do drink myself, but I would never drive after even one drink these days ... as if anything happened, I would always wonder if it was the drink which contributed (even if it wasnt) IYSWIM & might blame myself more than if I hadnt had a drink. (Not talking about being drunk ... just the subtle influence alcohol has.)
So I would say it's better to just NOT drink at all if your DH is driving.
Your only choice (when DH had been drinking and you don't drive and you wanted to go home) was to refuse to get in the car with him & to find some alternative transport home. (I know this was probably a tricky situation. And sympathise that you reluctantly let him drive.)
Is it possible you could learn to drive? If you have no disabilites and if you can afford to learn, driving is an essential life skill & knowing how to drive could save you life one day. So make learning a priority? Tell DH that you need to learn to drive now/pass our test/get insured ... to avoid the situation that he has to drive after drinking.
Whether you stay with DH or not, being able to drive would be very useful. So hope you can do that.
If you love DH and you want relationship to work, you could try to help him be a better person? Maybe he can be better with your help?
But if (one day) you see that you can't make him better (good enough) and you can't live with who he is (eg the drinking, bad judgement etc), then try to make you decision to leave him calmly.
No need to rush for the door yet? You have a young child, & no immediate place to go. So wait and see? Hope for the best ... that DH improves? Learn to drive/learn to take care of yourself & ur DD? Start to make some plans for the worst ... in case it comes to that?
But if DH is esssentially a good man, try to rescue him first? It might be possible? And things might turn out just fine? Don't try to tackle all his bad points ... just decide to focus on the ones which are critical to your happiness ... & let him know how you feel about these?
Good luck! Keep posting if it helps.