Happy to help.
I think it was the same bed - Papa Twist would probably have made grown Jack sleep in that little bed just to torment him. 
Oh BBM Fan.

As much as I think John Twist was not the best of fathers, I would think that he would not have deliberately planned this to torment Jack. I think it was just a matter of the room not being used that often anymore -- used only when Jack visited or spent the winters with them prior to BBM. Perhaps it was a matter of plain economics. Perhaps it was a preference for austerity.
After all, the Twist house was astonishingly bare. I can't still egt over the bareness of the living/sitting room. It is so cold and austere. It is probably a reflected the character of John Twist wore than it reflected the character of Mrs. Twist.
By comparison, Jack's room, though austere, looked relatively warm and personal. The little objects that were on the desk. The bench by the window. The tidyness and cleanliness of it all, in spite of the spartan decor. I think it reflected Mrs Twist's and Jack's softer, more loving characters.