This is a difficult one.
We all hate child abuse, but legally speaking especially when divorce and custody battles are involved it is a lot of he says/ she says. For the most part is seems like everything was fine until they dropped the investigation into his apparent child molestation. I would be curious to know why exactly, especially since the investigation was done by both the police and child services. managing to convince both to drop the case seems a little unusual for me. Of course that could simply be because the only one really providing any evidence of the child molestation is the mother, and if she was discredited enough it would cause those to evaluate her evidence with much more skepticism.
The whole process of discrediting each other though, it pretty common in the brutally ugly world of custody battles and divorces. I can understand the police dropping the investigation to a degree. I wouldn't be surprised if parents used false stories of the other partner abusing the children to get custody quite regularly, so it must be hard for the police to really sort the liars from the people who actually have an abusive partner. Especially when the truthful incidence of abuse is quite low.
This is a pretty sad story though, but not all that different from the ones where rapists are allowed visitation rites towards their victims children.