My father is an alcoholic. There is at least an element of choice here (no doubt will get flamed by those who think it's NEVER any fault or responsibility on the part of the addict).
In addition mil is an adult, dd is a young child.
Your job is to protect her - that includes from emotional harm.
Do you really want to teach her:
That you nor her father will protect her? From any harm emotional or physical?
That her emotional needs are less important than an adults?
That her safety is less important than mil's addiction?
That her role is to placate an addict? Even when they behave very unreasonably? (Bear in mind future consequences - future partners?)
That addicts don't face consequences?
That addiction is normal and acceptable?
Please take it from someone who had no choice - you must NOT facilitate contact when mil is drinking and I mean while she is still an active alcoholic, not just the few hours when she's hungover.
3 c's (also worth Wolfpac reading)
You didn't cause it
You can't control it
You can't cure it
The ONLY person that can change the situation is the addict themselves IF they really want to AND get the correct support.
Addicts will beg, threaten, blackmail, manipulate, lie, attack - anything they deem necessary to maintain their status quo as it suits THEM. They don't care about anything but maintaining their addiction.
Your dd is TELLING you what she needs, she needs YOU to make the decision for her because it's too great a responsibility for a child. You cannot make a child responsible for a very much adult issue.
Kim - using a child as a reward is completely out of order.
Honestly addicts are inherently selfish, that's why they can only quit when THEY WANT to.