I'm not a doctor of any kind.
even "obvious" answers shouldn't be withheld.
Torturing animals is often a sign of serious psychopathic personality disorders. This point is made clear in every serial-killer documentary on YouTube, and validated by this article I just found, which states just that, almost verbatim.
there are many types of IATC (Intentional Animal Torture and Cruelty), including individuals who do it... because they have psychological disorders (such as antisocial/psychopathic personality disorders and engage in deliberate acts of zoosadism), and/or (iv) because they have sexually paraphilic disorders (such as crush fetishism in which small animals are crushed for sexual pleasure). Additionally, there is some research showing that in some circumstances, IATC is sometimes used to coerce, control and intimidate women and/or children to be silent about domestic abuse within the home. Although any animal torture is shocking, arguably the most disturbing type of IATC is that which occurs amongst those with antisocial personality disorders.
Not all psychopaths are murderers, or even bad people though. The fact that your wife owned up to it and that she is concerned about your son leads me to believe she is not a bad person. She is probably dealing with the loss of your other son in a less than healthy way, but the obvious answer is that she needs professional help.
Logically, the best explanation for your son doing it is that he saw your wife doing it. We don't know if psychopathy is genetic or not, but I don't believe animal cruelty is.
The above linked article does give a little bit of advice, but keep in mind, this website and the internet in general are no substitute for real professional help.
There is no easy solution to childhood IATC. Given that most children learn antisocial behaviour from those around them, the best way to prevent it is teaching by example. Here, parents are the key. Prosocial behaviour by parents and other role models towards animals (such as rescuing spiders in the bath, feeding birds, treating pets as a member of the family) has the potential to make a positive lasting impression on children.
You may also find this article interesting: We think of psychopaths as killers, alien, outside society. But, says the scientist who has spent his life studying them, you could have one for a colleague, a friend – or a spouse.