Cloud confusion

Your description sounds as if you are using one Apple ID (ie. yours) on all your various devices, which is not recommended. What you ought to have is each family member with their own Apple ID, their device signed into their Apple ID and joined by the Family Sharing service.

If your wife has her own Apple ID (and therefore a separate iCloud account) then her device has no connection to yours. Furthermore, if you have your wife's phone number as part of your Apple ID it might account for her calls also being received on your phone. You can check this by signing in to your Apple ID account.

Are you using iCloud Photos? What mechanism is putting your wife's photos on your iPhone? If you are using iCloud Photos a deletion or edit of a photo on one device should also delete or edit that photo on all devices signed into the same iCloud account, so it sounds as if you are using some other method for the swapping of photos between devices.

I like to drain my phone physically once every 6 months to actually have the photo files stored on my hard drives

To what end? Are you creating a back up of your photos? Is this your only backup regime, or are you using Time Machine or a Windows equivalent? If so, then why do you need another archive? ICloud needs to be considered as an off-site storage of your photos in this model and your iPhone pictures copies of the originals.

I recently paid for more icloud storage

Excellent, but this won't give you more space on the iPhone. The extra space you have bought is for your iCloud account on Apple's servers.

I go into my phone and disconnect the devices to give my phone some autonomy when the reconnection thing happens

What process is this? Can you be more detailed?

There is a wealth of information on Apple's iCloud Support page which might give you a better idea of what it can do for you.