There are doggie doors that are radio frequency (or something) operated. It comes with one or two transmitters that your dog wears on its collar or harness. The door will automatically open when they approach the door wearing it. It is intended to keep unwanted visitors out, but it would probably help keep a kitten in, unless of course it sneaks out right behind the dog/dogs. There are several different kinds and brands. They are quite pricey though. Here is an example I came up with when I googled it.
Staywell Electronic Infra-Red Dog Door
That one is for bigger dogs, but hopefully they come in smaller sizes as well.