Sounds familiar. It sounds too like your mom was/is a very broken person or possibly has some underlying psychosis; I suppose maybe your forgiveness could be based on that. A lot of us, sometimes I think most of us (us in general not just poalers) come from unhealthy families. But we survive.
Consider who you are and what you've become. Base your forgiveness on that. Maybe your mom grew up in her own special hell; a friend of mine grew up with a violent alcoholic father. He hated his father until the day his father died then eventually came to realize and learn about the hell his father grew up with.
It's something you have to find for yourself. You don't have to forgive her but that anger and resentment is such a huge burden to carry.
Talk to your priest or pastor; going to confession may help you gain insight into unraveling your mom's chaos. I mention confession to help you with your idea of forgiveness and how to achieve it.
She grew up in a violent, alcoholic family, was thrown away to her grandparents at a young age, and she left her parents at a very young age
I'm sorry to hear that. Yeah, it's hard to forgive having a horrible childhood but, sounds like your mom didn't know what a good childhood is/was- she didn't know how to be a parent because she didn't have a healthy role model herself.
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