It is starting to sound to me like you and your mother need to have a long, serious, reality based discussion. There is plenty of factual information to be found about the the capabilities of the various species danger wise. The only two species known to eat humans as far as I know, and these are very rare cases, are green anacondas and reticulated pythons and your are not talking about these guys. Your mother's cat could be in danger from a larger boa. Other than that the animals you are considering are not really capable of causing any great harm beyond a nasty bite and most of the species you have discussed are not even capable of that.
If your mother is unwilling to consider facts beyond unfounded fears, there is not a lot you can do. Some people are just afraid of things and there is very little you can do to talk them into anything. Mom's house. Mom's rules, whether you agree with them or not.
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