Of course there is hope for you. You have two wonderful children and a grandchild and you are a worthy person.
Your mother cutting you off was her loss. Just like my mother cutting me off was her loss. That's how I see it (shrug). But maybe it was our gains. My mother at least was not nice to me, and I didn't need that.
I felt hopeless when they were in my life a lot, like when I was in my 30s, but have gently evolved to feeling loved and validated since, slowly, bit by bit, the FOO has become less a factor in my life. I had to do the final, terminal cut off with my sister to make it complete, but it is done with no other chances for her.Cedar, Copa and I have really gone into serious detail trying to figure out our FOOs and are all doing well. It helps to have others to talk to.
Your life will improve once you can focus on your positive loved ones and yourself too!!!!
Big hugs!!!!!