You are allowed to update all computers you own and operate. Trouble is she will always be dependent on your Apple ID for updates.
EDIT: If you choose to do that once your DL is finished choose to "install later" or just quit out of installer. Then go to your Applications find and copy "Install OS X Mountain Lion" to disk or to the other Mac to save DLing each time.
The 5 downloads pertain to content downloaded from iTunes, not the Mac App store.
You are allowed to download and install Mountain Lion on as many computers as YOU own and control. The license is tied to YOUR Apple ID forever and is not transferable, so you cannot use it on a computer you do not own and, your sister would never be able to reinstall unless you want to give her your Apple ID (which is not advisable). Also, for future consideration: as the license is not transferable, you must uninstall ML if you want to sell the machine, erase the disk, and reinstall the original OS.
The license states that you can download on as many Mac branded systems that you own or control. So can you honestly say yes to either of those in relation to your sister computer?
The other thing to keep in mind is that the OS will be tied to your Apple ID so that to download any any upgrades she will need your Apple ID or you will need to log onto the machine and do the upgrade.