The internal conflict of Duke Ferrara in My Last Duchess is very much left up to the reader to decide. It is a very complicated situation indeed. The internal conflict is the Duke being jealous of the Duchess and also being guilty for not being able to give up this jealousy after the Duchess's death. .
The Duke loved his last wife. There is a painting of her behind a curtain on a wall in the Duke's castle. This painting is covered so that the Duchess can only look at the Duke. He sees her as if she is alive in the painting and wants her to only smile for him. This is why he is jealous of her being " too soon made glad." The Duke was jealous of the Duchess's love for life and her easy-going attitude. He wanted her to love only him and it disgusts him that she could possibly have eyes for more than him. .
The Duke is selfish and inconsiderate in this act. He is telling the servant about this fault to relieve some of the guilt he feels. The servant, being a lowly citizen, will not tell anyone of this and at the same time the Duke can relieve some of his own feelings. He is more or less using the servant as a human diary. He recounts all of the things he loved yet envied about his love. .
When he talks about Neptune taming a sea-horse in line 55, he is referring to him keeping a curtain over his love. This way she can look at nothing but him and they can share this strange love together with none of the interruptions that might have been present during their life together. .
The Duke may also have been so uptight about life and upset at his wife's good looks verses his not so attractive features. This is why he poisoned her. He reached a point where he feared she might leave him because of his unattractiveness and her ability to turn ever head in the room. He could control this by making certain that she could be with no one but him. At the same time he could capture the feelings toward life she had that he wished he could possess.