tottered means "to sway from side to side", and is usually used to described the swaying someone might do before falling down. why would someone make a cat sway under a couch? it doesn't make sense.
unbridled means "unrestrained". this one isn't even a verb, so it definitely can't be used in the sentence.
coaxed means "to persuade". using this in the sentence would make it mean "she convinced the cat to come out from under the couch". that sounds like it makes sense to me!
