Honestly, I couldn't stay with a man like this.
Say in 3 or 4 years time, are you planning to lay awake all morning and night for him to get back?
What about if he gets back at 6 and decides to take your DD out in the car after he's drank and possibly taken drugs. Are you willing for that to even be a possibility?
The fact you aren't purely disgusted and running in another direction that he'd be willing to drive his taxi/van after drinking and putting others lives in danger is beyond me. I know you are upset and worried but seriously, doesn't that scare you that he can get like that at all?
Unless he admits he has a problem with alcohol, he wont get help. Without help, things wont change. I can guarantee if you just stick around this will happen again and again. I can almost guarantee you that your daughter will grow up thinking this is what happens in a relationship and possibly get in a relationship with a man like this herself. Because it can't be bad, because it's how Daddy is, so it's normal - right?
But if your daughter came home and told you that her DH was doing this, would you honestly say to just chat with him and see how things go?
I would seriously hope you wouldn't.
I am not saying you should necessarily end it forever with him although I would but to get yourself away and for him to see what he is missing. If he doesn't fight for you and DD, then he never loved you enough in the first place. If he fights for you both and finally realises that he needs to change, then you have accomplished something and things can move forward.
As far as his parents are concerned, ignore. You aren't in a relationship with them, so their opinions matter not one bit.
I hope you have the strength to take yourself away from this situation Off as hate the thought of you being stuck with this man forever and your daughter thinking acting this way is normal and OK.