Back when Airstream installed faux fireplaces in 34's (around 2000 model year..) they also included slim recliner/rockers made by Avant-Glide in Canada. They are stable, and swivel on a wood base, and have a patented gliding/rocking motion as well as a reclining back. They include an Ottoman with the same rocking/gliding motion...
I never bought the Airstream 34, but did just buy an Avant Glide chair, and love it... Here is link to dealer who sells via internet...
Gliders, Gliding Ottomans, Replacement Cushions for Gliders