After reading your post, I just wanted to send out a word of caution regarding the little girls speech and brain activity. My son is five and sometimes he states things that are just not right. He is doing it on purpose and therefore in my mind not lying about things. I just think his brain is not develped enough to understand what he is saying. Here are a few examples... He loves books and is starting to dream quite a bit lately. He woke up one morning a few months ago screaming at me to stop ripping up his books. I have never seen him this upset before nor had him talk to me like this. It took 30 minutes to calm him and show him his books that were unharmed. He could not understand that it was a dream. Another instance is he using the words "ask" and "tell" backwards. In other words he will say "Dad, I told mom what we will do tomorrow" when he meant "He asked me what we will do tomorrow. The final example is the whole family was shopping and my son was not walking very nice behind me. I ended up catching my shoe with his shoes and how we both did not fall down I don't know, but it ended up with him on the floor in the middle of the aisle crying because "I had made him fall down." I got the worst looks from people in the store because all they heard was a little boy crying on the floor because I had made him fall down. In no way was it my fault, but being 5 he just knows that I am still standing and he is on the floor so I must have done it. I try to explain each of these situations to him when they happen, but sometimes he just does not get it.
I applaud you for being so diligent about making the little girl safe and whatever other issues you have going on with her mother, just make sure you have independent facts before any accusations start. I have two great little kids myself. They are respectful and know how to behave, but they still have their moments and they just don't make the best witnesses. They take things out of context all of the time.
The mother lying on the other hand is cruel and is not going to help the little girl understand how to behave in an appropriate manner. The child must be so confused with different expectations at different locations. I also applaud you for trying to instill good values when the child is not getting that at other locations.