Do you think she should be willing to work for free and on her free time on your perception of feeling of contempt? Why do you think she should do that? Because there is a fair chance that she is not feeling contempt but for some reason you are perceiving it that way.

On the other hand, if you are certain that the T IS feeling contempt towards you then it is not something you can demand her to fix. Of course, it would be nice for her to fix it and then of course she should do it on her free time. But then the problem is more widespread for her and probably not much related to you and there's no reason for you to be involved in her process of fixing those things. The only thing you can do for yourself is to move on and find someone more professional.