I'm wondering about the diagnosis. If the boy is socially disconnected, has little to no empathy, then this could have been read as Pervasive Developmental Disorder (PDD) when it could in fact be part of something entirely different - a budding personality disorder coupled with Reactive Attachment Disorder (RAD).
An adult person I know (I no longer can call her friend, she's gunning for me, not sure why) used to confide in me in great detail as well as pick my brains about possible diagnosis. She has Obsessive Compulsive Disorder (OCD) and also very strong, detailed interests in some specific academic subjects on which she writes prolifically. She's also extremely religious (and at times attacks me for, as she erroneously claims, being a heretic). I blame myself for feeding her information about Asperger's. She went and talked her shrink into giving her n Aspie diagnosis. She told me afterwards she also has a diagnosis of schizoaffective disorder.
I looked up schizoaffective and especially as she became more unstable, I could see the Obsessive Compulsive Disorder (OCD) becoming more of an issue, and times in the past when she seemed more difficult began to make sense to me. I personally do not believe that the Asperger's label truly applies to her, but superficially she probably meets the criteria. But the schizoaffective explains it all too.
Medicine is an inexact science. Diagnosis always needs to be available to question especially when there can be other problems not fully understood.
Laughing over trying to kill the cat is not a Pervasive Developmental Disorder (PDD) thing in any way. I also wouldn't see it as a mood disorder issue. But it is a huge red flag for a number of other worrying mental health problems which need intervention NOW to try to "head off at the pass" the chance of the kid developing worse sociopathic tendencies as he heads towards adulthood.
The cat and the people in the home need to be safe. The cat cannot be there when he comes home. If necessary let your daughter take the cat and stay with someone else for a while - with her diagnosis, she is very vulnerable if he decides to vent his spleen on her physically. It was a very practical, sensible suggestion of hers.
A related problem - a good friend of mine was diagnosed with breast cancer, just as her youngest daughter was entering puberty. The girl went to pieces over this, on so many levels - her mother's cancer was a nasty one, fast-growing, so the chance of survival was not good. Mother and daughter was carrying the gene for breast cancer so this poor girl whose own breasts were just beginning to develop had to know that those growing lady lumps were almost certain to turn cancerous sooner rather than later. Seeing her mother go through treatment at such a time was too much. The girl moved out to stay with relatives for a few months. They are a close, loving family but the daughter was a huge mess at this time, having a lot to come to terms with at a time when her mother was the last person she could accept help from.
Good news now, 12 years later - Mum is cancer-free (although it was a huge struggle involving a lot of surgery, chemo and radiation over several years). Daughter is now grown into a beautiful young woman, very close to her mother and very loving. Of course they both have regular health checks, but it has worked out.
My friend let her daughter go at age 13, when she needed some space. It did no harm, probably helped. It gave them breathing space to put some strategies in place.
A different situation in a lot of ways, not so different in others. You have a 'disease' wreaking havoc in your home and individuals are in danger. Their safety needs to be ensured while you try to sort out what needs to be done.
As for how you can continue to love when they cross the line - I think that is how you know the line has been crossed; when you find loving them to be so difficult. I read your post to husband, and that is what he said.
Marg