Well, there are alternatives and choices and information to be had all around. First, it is reasonable to ask whether the child has seen an allergist, and for you to directly check with the allergist as to what precautions -- if any -- would be required to permit the child to not have a reaction (presuming that the whole thing is not being made up; if mom "just knows" that there is a problem with the cats, that is not good enough, and your son -- who I presume has joint LEGAL custody, even if for some reason physical custody is restricted -- can request/require adequate medical back-up.)
You say "the parents" are making demands -- your son is on board with saying that you have to alter your life because for some reason HE has supervised visitation? It might be more reasonable, every other weekend, to have your son reside at some other location at which supervision could be offered. Or move to eliminate or alter supervision. Of make some other accommodation.
You feel blackmailed because you are BEING blackmailed. I would do nothing to injure or dispose of creatures you love without first exploring every other physical, and legal, alternative. It may be a good idea for you, your son, or both, to consult with qualified legal counsel.
Answered on Sep 30th, 2014 at 11:45 AM