I havent posted in years, but this is unfortunatly very familiar, very painful situation to get yourself out of. For the sake and safety of your healthy relationship with Kat, it would be best to get Sue out of your home. If Sue is making the effort to get her finances together, I dont see a problem in helping Sue find her own place, even help her out finacially or connect with her friends and family if she is too unstable to take care of herself. If she has no family or she has burned all her other bridges then you might be in for some serious psychopath problem. Unfortunatly you will need to eventually pull away from her and even have a cut off date if you are helping her financially. Your ability to help her should be based on her ability to accept that things are not going to work out. If she is going to be unreasonable or becomes destructive, just cut her loose.
I can unfortunatly confirm that people dont really change, even if they seem like they did whether I help them, I get them to help themselves, or I cut them off and stupidly try to take them back. It's not worth it to maintain anything with someone who wants nothing more than to compete and sabotage your other relationships.
I wish you a smooth transition, but be prepared for some turbulence and don't forget your priorities.