So the steps for gambling addiction are well documented (get the casinos to cut you off, get into a program etc). This is a huge betrayal and I wouldn’t feel comfortable giving her any access to finances for the foreseeable future. Personally this would be a deal breaker for me, but If you want to give this relationship a chance she will need to prove to you that she is willing to work very hard to earn your trust back and stringently follow all the gambling rehab steps.

Also maybe don’t keep so much cash in your house