JMO
I have entertained the possibility that LV may have killed Charles herself, as well as Alx and the kids, and maybe even a prior husband or two, but when Tammy ended up dead, I think CD had a direct hand in that death to free himself to be with LV.
If LV used poison in any murders then I suppose its possible she could have had access to be able to poison CD's wife too, but if that had happened then I think CD would know about it and was directly involved anyway because he wanted to be with LV anyway and he would be aware of the others being taken out because it was CD himself that declared some of them as zombies. He even predicted that Tammy would not live long.