Dear Sad and Scared,
I'm sorry to hear about your idiot husband.
I guess my first reaction to your situation is why would you want to continue to be with this guy? I don't agree with those who say that it's best for the children that unhappy parents stay together.
Your problems with your husband are really not about your niece.
Sex is Usually a Symptom, Not a Cause
You mention that you have turned him away sexually. Usually, if I understand women, that's a sign of dissatisfaction in other aspects of the relationship. It sounds like that instead of dealing with it, you two ignored the real issues. Sex is not the goal, it's part of the process. If other aspects of the relationship were suffering (communication, goals, financial issues) then you really should have focused on those.
It seems like guys say, "I need sex to show how much I love you and get closer to you." It seems like women say, "sex is a special thing we share when we are really connecting. If we can't connect in those other ways, I'm not that interested in sex with you." That fundamental difference means that both partners have to work. He needs to connect better to you, and you should see that for him sex is his favorite way of connecting (as if you didn't know that.)
So, yeah it's really embarrassing that he's fooling around with your brother's daughter. I wouldn't stand for it. In fact, I probably wouldn't even try to get back together with the guy. On the other hand, the problem isn't your niece, it's between the two of you. Don't blame her for issues that you need to reconcile with him.