Multiple user iCloud accounts on same computer
In your account on your partner’s Mac , open the system preferences and turn off iCloud for photos and documents or sign out of iCloud and let the local copies of your data be deleted. 

Then if you sign in again, skip the automatic, sync all option and only choose items you need. Photos and documents can be allowed on a space available need or you can just leave all that in the cloud. Choose to optimize the storage if you can. 


https://support.apple.com/en-us/HT208682 (iCloud setup)
https://support.apple.com/en-us/HT206996 (Optimize Storage)


You can enable settings so only a portion of the data downloads: 

Having more iCloud space than actual disk space (on macOS)?

If both accounts enabled optimizations in the manage settings for iCloud, it might work to have all things turned on for full iCloud for both of you.