Tammy Grimes was a very talented stage actress who became famous for starring on Broadway in "The Unsinkable Molly Brown". Unfortunately, her lack of box office fame was why the movie went to Debbie Reynolds instead. Tammy had some memorable guest shots on "Route 66", "Burke's Law" and other programs in the early 60s that are worth a look.
She was also briefly married to Christopher Plummer in the late 50s. Actress Amanda Plummer is her daughter.
As for the sitcom, it was the sort of thing that might have worked for a play or a movie (it was created by George Axelrod, author of "The Seven Year Itch" among other things) but as a premise for an ongoing series, it was totally unworkable. All you have to do is watch the one episode on YouTube to see why it couldn't have possibly lasted.