When we are dealing with someone like that, manipulative and a liar, it is my experience that we, the nice people, usually hang in there way too long and continue to show our soft underbellies only to have them ripped again. This type of person takes advantage of that.
It is great that you had the courage to write the letter. It was an accomplishment. Be proud that you expressed your feelings. You will need to get that affirmation from within yourself though, because this person will not respond in a positive or reasonable way. They may well, in my experience, be incapable of apologizing. Many liars also lie to themselves! Acknowledging what they have done to others means having knowledge of their real selves that they can’t tolerate in their fantasy world.
If you really are ready to move forward, you will have to be firm about the new boundaries you have created. I know how hard it is when it is family, because it is never just you and that relative. Everyone else chimes in, takes sides, etc. Plus, there are holidays and other family events. It is very hard, but persevere.
Your peace of mind and not having that sick feeling in your stomach before (will there be a big scene today?), during (it is like waiting for a bomb to go off) and after encounters with this person will be worth it!