Me - A U.S. citizen
Wife - A British citizen
Stepdaughter - A British citizen
Unborn daughter - U.S. citizen
Cat - A Stateless national (He's a Persian though so probably Iranian!) 
Once the unborn daughter arrives, and you've gotten her UK birth certificate, don't forget to register her birth with the US Embassy, and order her US passport. This will require a trip to London, or Edinburgh if you are in Scotland as you can file the paperwork by mail, but it must be finalized in person.
(There are existing threads with more detail.)
And, documentation for the cats vaccination shots will vary by state, so make sure you have records for that. Not as complex as coming to the UK, usually just the paper work and your word that it's the same cat will do it. Microchip not required.
Good Luck
