Sounds like there is a lot of dysfunction in that family. A lot of denial and lying also seems to be commonplace. It's good that everyone is collecting evidence of what is going on through Skype and all. It will help A's situation if there is some hard evidence of what is going on. It is so hard to tell as a social worker who is lying and who is not. But you have some very good evidence to back up what you are saying. I hope just based on that alone, this case goes quickly and A's parents lose custody. I really do not think counseling will help her father or mother in any way.
That is ok. I just mentioned that because it didn't sound like either one is open to changing anything. From what you said, they both seemed defensive and neither saw what they were doing to A as an issue. People who do not think anything is wrong do not usually do well in therapy because they are not willing to change.