First, please excuse that I am oversimplifying this greatly. Start with your heart, and the core question of "what do you really want
for her"? Once you have a very short list, outline a specific set of actions and backup/contingency plans that go towards those goals. Then define the items that you are willing to give up (or personally tolerate/endure) to make that happen. You can change things in the divorce decree if everyone agrees, or if no one disagrees (keep documented agreement, though). As an example:
1. Want girlfriend's daughter to have positive relationship and interactions with her father.
- Define the set of conditions required for this to happen, and propose actions based on when the situation is not conducive to a positive relationship. For example, agree that in the best interests of the daughter, you will assess his condition when you drop her off (i.e., no more grandma pickups) and she will not stay if he is drunk. Also agree that she will be picked up if Dad becomes drunk, and visitation will be done for that week.
- Are you willing to drop the issue of collecting child support if this is agreed upon by Dad? If so, that's your bargaining chip to get his consent. If he's as selfish as he is portrayed, this shouldn't be hard. As long as the daughter is taken care by your family, the benefit of the unpaid child support may not be worth the constant battle. You aren't getting it now, so you aren't really giving up anything.
3. Want positive relationship with grandma
- Establish grandma activities and times where they can interact without drunk Dad (i.e., outside of house where Dad lives). Remove her from the equation by giving her the time with her granddaughter. Invite her over at some frequency (e.g., dinner/outing every two weeks). If you really want this for the daughter, you might have to put up with a bit of crap for her benefit.
Just holding up a mirror a bit, but there are lots of sour grapes raised in the posts that have nothing to do with the best interests of the daughter. Get out of the trap of telling stories about grandma's money and child support you aren't getting. You want her to be able to form good relationships when she is older, and not have Daddy issue baggage for years to come. If she were to see him when he isn't drunk, that may be a good starting point. If what you really want is different (e.g., Dad out of her life completely), then clearly the actions can be radically different. Best of luck!