This is tough because she does have rights. You've been handling this well, so far. Do you have POA for health care? If you don't it should be done now (don't mention the marriage - just that she will need you to help her with health decisions as her AD gets worse. 

What is this man's attitude? Yes, he's nice, but he may not want to marry someone diagnosed with AD. If worse comes to worse, tell her to keep the house but to move up and live with him for awhile. That may settle the whole thing.

Unless she has a lot of money (and if he wired her money for her car, it sounds like she doesn't) he likely won't be willing to take on the medical obligations (bills) that will go with her care if he marries her. Can you talk sense to him? Suggest that they just be friends?

They are both likely lonely and do like each other. That doesn't mean they have to sell her house and get married. Try for an even bigger compromise than you've done so far. Other than that - she will do what she will do unless you get a court order to declare her incompetent. That would be hard to do at the stage. If she insists on trying to sell her house, maybe you'll get lucky and it won't sell before she changes her mind and comes back.

Let's hope he has more sense. Perhaps a visit of a week will take care of the whole marriage "threat." 

Obviously, if you don't think she is safe doing even this, you'll have to try another angle, but it's the only solution I can think of. Good luck!

Carol