I studied Chinese and anthropology in college and have recent started to really research the historical connections between Tibet and Mongolia. I've learned some of the claims China made to take control of Tibet in 1949/50, but what claims did China make to control Inner Mongolia as of 1957?
One must take in the fact that while Tibet has been ethnically separate from China (even now having a 90% Tibetan ethnic makeup), Inner Mongolia's population was almost 84% Han Chinese in 1947 (it's actually decreased to 80% in the present day). Of course this does not answer your question, but the two territories had a vastly different situation when "annexed" (also not technically a correct term to use here).