Your family situation is a very very painful one, every years it becomes worse and worse, and personally I do not think that to have it on TV helps.
As seen on the RHOC, suggesting something (like for instance that your sister has a shady work in a shady bar) is as hurtful if not more hurtful than to say it. Repeat after me: Suggesting something is the same as saying it, repeating a rumor is the same as starting it.
Melissa is not the forgiving kind. It is her choice. Register the info and move on. Do you really think you will need her absolution? Why does her opinion of you matter so much for you? Why do you give her so much power? That is your choice dear.
Insults hurt first the person proffering it. I know it doesn't look that way at first but it is. It tells other how much self-worth a person has for herself. It shows how powerless a person is. Insults come when communication has failed. I do not means this lightly. You guys do not know how to communicate effectively. It is obvious, from the get go, you do not listen to each other, you do not listen to what you say (I mean you in a collective way), you do not take time to digest what is being said, before reacting, you do not pay attention to intentions before reacting. In one word you do not communicate, you declare stuff at each other.
They called you names, that doesn't change who you are. If you are the one insulting it odes change who you are in a deep way, it makes you a powerless person unable to communicate your feelings and resolve conflict. Worse, it makes you the one who hurts or who tries to.
Be always the bigger one.You will teach your children how to be good, and that is something worth fighting for.