I"m not sure an ultimatium is a good idea, it may pressure her to make a decison, if she chooses the psychaitrist she could end up resenting you for it, if she chooses divorce it may put both of you in a rough state, I would say only choose the ultimate if all else fails

Maybe marriage counseling instead? Or an intervention by family and friends? Or explain to her you don't think she is crazy but just needs help, mental health is just as important as physical health and seeing a psychatrist is like seeing a general practioner, expcept for illness you cant' see with x-rays or blood tests. sometimes people are afraid of what they don't understand, do research to inform her and help battle her fear.

Another idea, have you tried showing her the destructive effect her behavior is having on your marriage and her?

I hope all works out medicnh and keep us updated on how things go.

Best Wishes
Typo