The only way for you to have the same photos in these two different versions of iPhoto without an extra tool is to export them from one version, then to import them into the other. This may result in a lot of additional manual work to rearrange events and albums, etc.
A tool that should work for you is iPhoto Library Manager. You are within its minimum requirements for both OS X and iPhoto, the app is well supported and works flawlessly for me. All you need is having the two Macs on the same network - preferably a fast and stable one (wired Gigabit Ethernet, if you can) as IPLM will move a lot of data back and forth.
With IPLM, you'll only need an iPhoto Library on either Mac, the complete, maintained one on the iMac, and a new empty one on the Mini (created with the iPhoto version on the Mini). Then you "merge" them with IPLM. Check options an preferences carefully before you do so, though.
Later, as you apply changes or add photos to either library, you can merge them again easily. Again, double-check prefs carefully first as different settings than the first time might be required.
