I don't think she has a moral right to know the details of his inheritance, though I do believe that it is more healthy for a couple to be open about their finances. I don't believe she has a right to have access to his business account, either moral or any other right. A business is a unit of its own, and it is probably a private or a public company. The fewer people who have access to the account the more secure it is.
I suppose it depends what she means by "access". I have assumed she means access to the money in it, but perhaps she just means she wants to know how much it is worth. It sounds very much like a Victorian papa enquiring into a suitor's prospects to make sure he can keep his daughter in the manner to which she would like to become accustomed.
Anger management!!! Help needed.