Not to jump into a debate here, but I've been in your situation. It really stinks but I think your going to bite off more than you anticipate if you call child services.
I was there -- 19 years ago when I met my DH. He had just gotten divorced and was paying $600/month in child support -- 19 years ago that was ALOT of money to pay. When we got married, his ex had a big problem with it and caused our lives to be a living nightmare. His ex put us through the ringer with courts and lawyers and accusations which were not true. In the end, what did it do?? Turn a loving father/daughter relationship into one which was never repaired. It's been years since my DH has seen his daughter. In the end, his ex got what she wanted, but it wasn't until many heart breaks were felt by all of us. We can only hope that someday my step-daughter will choose to come back into our lives. We are still waiting with open arms.
The things you have said here, while may not be the best choices for a 10 year old, are not anything the child is not going to encounter. You are looking at this drinking situation from a 10 year olds eyes -- do you know the parents who were going to watch the kids? Just because they were (maybe) going to have a couple of drinks, doesn't mean they can't watch over the kids.
We have lived the nightmare. I think you need to consider the accusations your making here in the correct light. While they may not be your parenting belief, it doesn't seem as if they are affecting the long term relationship between your fiance & his daughter. Calling child protection services could affect that big time.
Also, if there are medical needs which need to be taken care of for the child, your finance should be making sure they are met. IMO, he's just as guilty that a child didn't get the dental work done which she needed -- regardless of whether he was paying child support or not!