Hoping to import exotic pet for kids

I have been having a hard time finding any information regarding the import of “exotic” pets to the Cayman Islands. I have searched the agriculture documentation but was unable to find information regarding primates (specifically marmoset, capuchin and sugar gliders) and also miniature pigs. My kids have recently visited a family in the USA which has had these as pets and fell in love with them. I would like to be able to get one for the children. Please let me know if you have any information regarding this.

Read Auntie’s answer and comment on CNS Local Life