Alison, 50, said: “I want to reach out to my sister and tell her how much I miss her and how proud I am that we are family.
“We may be apart now, and it has been many years since we last spoke. But to me, despite all the bad times and the arguments, she will always be my baby sister.
“I cannot put into words how moved I was to see pictures of my niece and nephew for the first time. I saw photographs of them on the television just after they were born and I saw more when they turned one recently.
“I am sure Mariah is going to be a fantastic mother and her husband Nick Cannon, who I’ve heard nothing but good things about, will be a great father.
“I just wish Mariah would let me be her sister again and a proper auntie to her children.
“I know we have had so many problems over the years, but I want to reach out to her in the hope that we can make peace and mend the wounds that have torn our family apart.”
The 'Fantasy' hitmaker promised her dying father in 2002 that she would end their rift but they have spoken just once since then.
Alison - who is HIV positive - told The Sun newspaper: “She has never met that promise. I last spoke to Mariah four years ago when she called me on New Year’s Eve. But since then I have not been able to speak to her.
"I reached out to Mariah last year when a doctor told me I had liver cancer and only four months left to live. A relative told me Mariah decided she wanted to reconcile and she would pay for my treatment. But I never heard from her.
“It turned out to be nothing more than a gallstone. But it would have been nice if my sister had been there for me.
“I’ve had my problems over the years but I want to tell Mariah I have been clean and sober for four months now and I am absolutely determined to keep my life on track."