We put our dog to sleep in May 2007, our daughter had just turned 2 on the 28th of April that year. She was a very sick, old dog. Very sweet, but generally was sort of "whatever" about everything. She was an abused stray when my husband adopted her so she was very wary about jumping and barking and licking and so on, so she and my daughter didn't play much really. Besides the point my daughter adored and loved her. One of our bestfriends is a vet so we had told her that Aunt Alissa is a puppy doctor and Trixie is very sick. She is going to live with Aunt Alissa because she knows how to take care of sick puppies and she will probably not be coming home. She did ask questions for a few days, maybe a week, of where the dog went. Eventually she stopped. She forgot and when she was about 3 and understood what death was she started asking again. It didn't seem to scare her but she more so seemed to have put 2 and 2 together.
We keep a 8X10 picture of Trixie with her collar and tags hanging off the frame on our end table and my daughter now knows she died. At 3 yrs 8 months she has the emotional understanding of death and accepts it pretty well. She has, unfortuneately accompanied my husband and I to a few wakes. When she was 3 months old my best friends mother passed away. And in the summer of 2007 one of my childhood best friends passed. They each lived on either side of me growing up. I would not let her near the casket nor would I go near it myself. But she understood that people were sad and she just tried her very best to make them smile. I though the same way you did but you probably are looking a little too far into it. They probably won't be all that concerned as you think they will be. If I were you, I would tell them that "Kitty is very sick and she may not be around with us much longer." If you are religious, you can tell them the kitty is going to live with god now. I've heard some people do that. You don't need to give them too much information. But try to give them the truth in a way they can understand. I know this is a horrible time and I wish you all the best. Good luck with everything.