There is an excursion that goes to Johnson space center then takes you to airport (IAH) It does start at 9 though and is four hours so may be tight for your flight….but you might look for something like that independently
Check with the hotel to see if they provide car seats….or if they require them and require you to bring your own. If it is a Washington state law, the hotel shuttle may require. If they do, see if you can rent one in Seattle.