Re: Is it normal?
She is using her right if she is demanding this. But the way she puts it is strange and is creating bad feelings in you for her. Try to discuss your feelings with her and tell her that really would like both of you to work for a happy marriage and she should really reconsider her decision of marrying you if she doesn’t trust you. Afterall, trust is an important factor for marriage and if trust is lacking, its not a good start to the marriage.
If she would have put this demand by telling you that she wants her future to be secured because of high incidences of divorces these days and would try her level best to make the marriage work, it would have been better.