MobileBackups is using too much space I am running short of space on my OS partition for some large files I want to install.

I note that du shows 15G /.MobileBackups
I have 2 Time Machine drives. One attached to my MacBook Pro (at least when it is not being used as a portable), and a second, which is attached once a week. This was last updated yesterday.

What is using the 15G and why? What would happen if deleted it?

A second issue. du shows 103G    / but Disk Utility says Used 112G. Is this the sum of file sizes vs disk space used?
Mobile backups are a part of Time Machine called "snapshots" basically it lets you restore to one of the most recent backups without the need for you time machine disk. 

I believe OSX will automatically free up this space when it is need, but it can be turned off manually as well. 

See https://support.apple.com/en-au/HT204015
And http://osxdaily.com/2011/09/28/disable-time-machine-local-backups-in-mac-os-x-lion/