You aren't responsible for their relationship. Your ex clearly had no problem drinking and driving with her in the car, which shows how little regard he has for your daughter and her safety.
Something that has been hard for me to let go of was the hope that my ex would do right by our son. He is not entitled to have a relationship with our son if it means exposing a young child to dangerous drunken behavior.
I am the daughter of an alcoholic. My mom stopped forcing me to go over for visits when I was about 14, but a lot of damage had already been done. I haven't spoken to him in almost 20 years. I thought about reaching out when my oldest son was born, but my dad had moved and didn't leave any forwarding address or way to get in contact.