If your partner's sibling doesn't want to stop, he won't. End of story.
You're not married? I would separate my finances as best I could, take the child, and move out. Co-parent the child in a civil manner. The longer you stay together, the more entwined your lives will be.
Your partner *should* have the best interests of his partner and child at the top of his priorities. He doesn't. Your child is learning that this is normal, and that "lying, manipulative, sexist, homophobic, egocentric and racist" are acceptable traits. BIL does not have an issue with his drinking. His mother doesn't have an issue with it, his brother doesn't have an issue with it. YOU do. In his family, this is normal behavior, and your daughter is learning it is, too.
Compassion isn't the same as being a doormat.
How do you support someone who won't stop drinking? Gee, stop buying booze for someone that can't function on his own would be #1, if he can be detoxed safely. If it's that important, don't have alcohol in the house. Don't pretend that this is normal.
You feelings and intuition are normal. Your MIL and partner likely think of themselves as compassionate saviors of this chap, even while they help him self-destruct. I can bet what their attitude is: "His wife and friends have abandoned him, but we can't! We won't! he's family and this is what family does."
Not all families.