I would definitely not tell them that the cat is being put down. We
went through this a few years back with my parents' dog, who my DD was
very close to. All we told her was that he was very old and sick and
he died because of that. I know if we had tried to tell her about
putting the dog to sleep, we would have heard "You killed him!" I just
don't think that four-year olds can understand why this is a humane
thing to do to a pet! Because the kids will know you are taking the
cat to the vet, you may just want to tell them that the vet tried very
hard to make her better, but she died while she was there. That is all
they need to know until they are older.

I am sorry your beloved cat is sick

Ellen