What bothers me are the conflicting stories. From your version, this never happens at your house and you have never seen it happen? Its not easy for a child to act one way at your house and then act completely different in another place. How is he at school, for example?
The only info you have is what your 6 year old daughter has seen/felt? What does your ex say. It would be very hard to believe that the ex would allow her daughter to be treated so badly. And from what you have said your ex has never seen it happen? Which also makes me wonder about the statement that, " he smiles and laughs as she crys." If neither adult has seen this happen, then your daughter must be reporting this? As margypops said, the dynamics here are a mess. Sounds like you have two households and probably two kids in conflict. Actually, you could have two kids in competition for attention. Wondering if the kids are caught in the middle. How does a boy who was "kind and sweet" go the other way? Before, I call child protective services, I think a bit more reseach needs to be done. If the facts bear out that he is abusing her and that the other parent is allowing this to happen, then a call to the services is probably necessary. Proof of the abuse however, will be tricky. Good luck.
Totally agree with paperclip, the dynamics here send up a red light ....
The child is too young to give such terrible labels to, especially as he has been through so much. You as a family need to see a therapist and work out how best to handle him.
Get Dr Phils book on familys or contact him, he has such good advice for children in your sons situation.
Have you considered a personality disorder? Many people with these disorders have little to no conscience or able to feel empathy (and I feel personality disorders are a genetic/inherited trait). But, there is research going on in this area with some therapies (very little medication yet) which can help those suffering from these mental health issues. A sociopath or narcississtic or histrionic would be three personality disorders which fit the criteria of "little to no empathy". There are also others. Please contact a medical mental health specialist as a child psychiatrist or child neurologist to better guide you in this journey. All the best ....
Talk to an attorney right away, and/ or the local child protective services.