Danger!
Warning!
BEFORE you upgrade them, you should realize that Apple's "modern crop" of OS's -- from Mavericks on up through Sierra -- seem to have been engineered to run best on Macs that have either an SSD or a fusion drive.
This isn't to say that El Cap won't run on an older Mac with a platter-based hard drive -- it almost certainly will -- but what you may find is that the "running" seems more like "walking" on the older hardware.
I realize that the "perception of performance" is an individual judgement.
What I sense to be "slow", may be acceptable to others.
If you want to "spruce up" the gf's parents' computer, my suggestion is.
1. Create a cloned backup using either CarbonCopyCloner or SuperDuper.
2. Boot from the backup
3. Re-initialize and test the internal HDD using Disk Utility.
4. Install a fresh copy of 10.6.8. Or perhaps 10.8.5 if it will take it.
5. At the close of the install process, use setup manager to "migrate back over" their accounts, apps, data, and settings.
Do it this way, and it should "clean up" the internal drive, which has surely become fragmented over the years of usage.
The re-install should clean up much of the fragmentation, and also create a large contiguous area of free space on the internal drive, as well.