Only a Westerner would ever think China wants Mongolia. Trust me on this one: if the industrial revolution hadn't happened and we weren't living in modern times, China and Mongolia would be perfectly content living in complete separation of one another. From a more modern perspective, there simply isn't anything Mongolia has that China might want. Mongolia is like Iran on steroids— a bunch of mountains and steppes. Except unlike Iran, Mongolia is located in an undesirable place. No major trade routes run through them, no major crops are grown there that can't be grown elsewhere, no major industry relies on them— for a nation formed by what was once a stateless group of nomads, this is perfect because it means no one will mess with them.
There are more Mongolians in China than there are Chinese in Mongolia. After all, there's an entire province in China known as "Inner Mongolia". That's about as far as China even wants to go.
So to be clear, the only reason China would invade Mongolia is if, in order from least to most likely:
- Unobtanium is discovered in the Mongolian steppes
- China is run by an ultranationalist expansionist who has lost touch with reality
- Mongolia itself invades China
Yes, that is the most likely cause of a Chinese invasion of Mongolia. I personally wouldn't want to be on the receiving end of a modern Mongol horde, but times have changed and the only reason China would risk their relationship with Russia over Mongolia is if some serious alien space bats took place.