You need to change the wording you are using in this situation.
You say in the title you are ‘abondoning’ her.
But actually, that is what she did to you. She, the mother, abondoned her child on many different occasions over a number of decades.
What you are doing is not abandoning, but seeing the relationship for what it is (non existent, toxic, detrimental to your health, protecting you own child, unlike what she did, and living your life healthy and happily inspite of her, not because of her)
You are not abandoning anyone. But you are putting up boundaries to protect yourself and your family.
Don’t worry about other people believing her lies. That’s on her, not you. You know the truth and they don’t matter.
Start by looking up what the greyrock technique is and applying if necessary. Don’t be available for her ‘holidays’. Get rid of your answering machine and have caller id. Don’t answer the phone when it is her unless you want to.
Start limiting contact and see how your life is. I am betting NC won’t be far.