My mother & my cousin

I won't go into the very long history but my mother came to live in the house next door to me; she said that once she'd sold hers she would pay for this although I had to remortgage my home initially. This was about 13 years ago.
Once installed I found that my whole life had been a lie. She had abused my brother - again, I won't go into details except that she had only wanted daughters.
Once I did find out I broke down - my friends at church were great; my family was supportive but added loads more details to this person who had lived a lie for so long. She was extremely clever at telling which lies she told which people!
When I mentioned a certain fact to her she just looed at me and said'You've been talking to brother". I still worked at that time and came home one day to see that a cousin had come from Wales and moved my mother out. Not a word to us. I was eft with the mortgage, which was the first thing I paid off when I retired - nothing from my mother.
I send greetings and tried to keep in touch, but have heard no one word from my mother.
My daughter and her family have been living in the house, but we are now trying to sell both. My cousin has sent me a letter saying she'd like my new address;I sent an Easter card to my mother saying that we were hoping to move and that I'd continue to send her cards but not send her my address as she'd not contacted me, my brother or any of her grandchildren in the intervening years.
I do not want my cousin to have my address - what do you think?