The main conflict in A View from the Bridge centers around an uncle's fear of abandonment. He's terrified of his niece growing up and moving away. On the flip side of the equation, the nice is terrified of leaving him. When these fears aren't confronted in a rational way, they end up damaging an entire community.
It's hard for Catherine to abandon Eddie because he makes her feel safe. She's comforted by the iron-fisted control he has over her life.
It is Eddie's fear of abandonment, not sexual desire that drives his irrational actions.