Why was the duke unhappy with his first wife? What does this reveal about the duke and what does the poem title suggest about his attitude toward women in general?

In the poem, the duke was unhappy with his wife for a number of reasons. First of all, in lines 14–15, the duke says that his wife often blushed at others. Specifically, this "spot of joy" on her face (a blush) was caused by things other than her "husband's presence." She might blush at a sunset, for example, or some "cherries" brought to her by a "fool."
In the next few lines, the duke argues that his wife was "too easily impressed" by the people around her. Moreover, she seemed to find happiness everywhere and in everything:

She liked whate'er she looked on, and her looks went everywhere.

Furthermore, the duchess did not distinguish between the gifts brought to her by her husband and those brought to her by servants and strangers. She treated everyone equally and did not elevate the gifts and conversations of her husband above those of others. An important example here is the "nine-hundred-years-old-name": the duke thinks that his wife should have been grateful to him for elevating her to such a high social status through marriage. But she did not reciprocate this feeling.
In other words, the duchess did not live up the duke's expectations. From these examples, we see that the duke wanted a wife who was totally dedicated to him, and him only. He wanted a wife who appreciated her social status and thanked him for it. Moreover, he wanted a wife who understood that her title of duchess made her socially superior to those around her.
The use of the word "my" in the title suggests that the duke feels a sense of ownership toward women, in particular his wife. In his mind, women are objects and ought to behave in a very specific way--a way that is constructed and sanctioned by men. In addition, the hint that the duke may have murdered his wife shows his inflated sense of superiority: he believes that he has the right to end her life because she is not as valuable or important as himself.