There's been a few threads on permies about this but I haven't seen one done inside a moveable tiny home sucessfully yet. As Ron mentions weight is an issue, both for floor strength, and for driving/legals. One way to solve the latter is to make something that is removable.
Other issues are size of mass in a small space, best minimum flue size for efficiency (there is info on this in past threads), and safety/design.
I considered this for my housetruck (similar size to your tiny home) but fast and direct heat suited my situation better so have a conventional
wood stove (with fire bricks inside). A RMH inside a tiny moving home would need good design and experimentation to get right. I think someone will eventually do this, but the RMH material I have seen is aimed at efficiency in spaces that are quite different to mobile tiny homes. I would love to have a more efficient
wood stove so that I burn less
wood, and can see a
rocket stove being in such a small space, but the mass will always be the design sticking point. Maybe someone will develop a hybrid that ups efficiency but sacrifices some of the mass as a concession to weight and space.
Just looking at the old threads, Erica Wisener says that RMHs in tiny houses are using 1/2 - 3 tons of mass. That's about 3 x the weight of my full sized woodburner, and not an amount I would want to add to the house.
https://permies.com/t/14609/wood-burning-stoves/RMH-flue-fires
Another option is to build mass into the tiny home that serves dual purposes.
https://permies.com/t/28910/wood-burning-stoves/Mini-Pocket-Rocket-Van-life#231392