I guess I don't use the word "abusive" in the sense of being deliberately mean. I tend to believe people are basically good. If they hurt or abuse other people, it's because they're in pain themselves. They're trying to get some relief from their suffering. They may or may not be aware that they're inflicting pain on other people. They may or may not care. And if you tell them they're hurting you, they may or may not stop. They may or may not believe you. They may or may not be able to stop - even if they want to. By that definition, your mom is abusive.
I don't think my son was setting out to be abusive to me, for example. He wasn't thinking, "Wow, I'll hurt her with this!" He was angry or in pain himself, and he tried to get some relief by yelling and accusing.
Your mom reminds me a bit of one of my mom's friends. My mom is 81 and basically all the people she knew when she was young have died or become so disabled they're mostly homebound. So she's tried to find new friends to do things with. One is a lady named Theresa. Theresa is a depressive, so it's hard to be around her. She complains all the time. She makes racist comments which make my mom uncomfortable. But the worst is she's constantly correcting, disagreeing, and arguing over every little thing. I feel so sorry for her. She's a widow (doesn't miss her husband, though, because he cheated on her) with two surviving sons (one died at age 25).
Her sons will have nothing to do with her. She complains about them all the time. They can do nothing right in her eyes. The only one she actually seems to like is the dead one. They both live in the same city with her, but neither invited her to their houses for Christmas last year. One moved to a different house without telling her. She only found out because she happened to drive by his old house and saw a real estate agent's sign in the yard. She thinks he may also be divorced, but she's not sure.
I feel so sorry for the woman. She's driven everyone away. Even my mother can barely stand to be around her. She just needs someone to do things with, so she tolerates her.