How to stop Family sharing on an old Apple ID?

I had an old Apple ID and started Family Sharing with my wife. I had to get a different Apple ID and now that I want to do Family Sharing with my wife, I have to undo it from the old one.

My problem is that if I log out of my current Apple ID on my Mac, it will delete files so, I can't log into my old Apple ID on my Mac. Is there any other way?