Im a Carpenter,
Steam bent wood will retain its shape, you just need to follow a few rules, once it is bent to shape, it must be dried out, if you started with nice kiln dried at about 14 % or less moister you need to dry the piece out again, this dosent take as long as green wood as the wood is now a skeleton, not a living thing anymore the cells will not accept water back in, thats why wood floats for a long long time before sinking. also there are excelent glues on the market today, epoxies, and one i would use for this, resourcanol, spelling could be wrong, its a powder and a liquid mix, ive glued two pieces of oak together with this without clamping, and the next day not be able to break the joint beating it with a hammer. next you want to completly seal all surfaces, as not to allow any humidity or moisture to react with it both sides, heres why, if you have ever looked at a house that has shingles that are cupping, this is because the back sides of the shingles were not sealed, only the fronts the front side gets the Sun, and is sealed, so it just stays the original shape, but the back side soaks up moister and expands while the front stays dry. Also, most rocking chairs rockers are cut out of a wide board, or glueups, being on the floor and scraping on the floor would open the wood and be more apt to take in moister and unbend, also remember that wooden boats are built "old shool" with steamed bent wood, they steam it and bend, and either peg it down, or use screws, or glue, a sealed seaworthy boat just dosent unbend when you put it in the water. Hope this info helps in your decisions. good luck!
Tidy