This is similar to bailor/bailee law. Your cats are your property, and you have hired someone to take care of them. Should that person deny you possession, they have switched from being a bailee to a person claiming possession, which is conversion. If the cats died [unfortunately], and you suspect that they were mistreated, the wrinkle is that, as you may know, there are laws protecting the cats, and the police may be involved to investigate such mistreatment or prevent such mistreatment from occurring.
Putting the cats in a shelter without your permission or knowledge is akin to conversion.
Therefore you have a number of legal remedies.
