Your mother is fortunate, indeed, to have a son who is interested in understanding rather than simply rejecting her. Her behavior must have been very hard on you and your father while you were growing up. Please understand that her attitudes toward you have nothing to do with you personally. She is caught up in her own issues.
I can’t ethically make a diagnosis on the basis of a letter alone. However, knowing what you have told us, if I were to see her, I would be evaluating her for Borderline Personality Disorder. Someone with BPD has difficulty regulating emotions and has unstable relationships, often going to extremes, loving someone, then cutting them off for minor offenses. I suggest you search the internet for more information about BPD and see if it fits.
Regardless of the “label”, your mother has been in deep distress most of her life. She needs help beyond what she has been getting. I suspect it will be difficult for her to stay with one mental health provider for the same reason that it is difficult for her to stick with a friend. If the provider says something she doesn’t like, she will probably leave.
If your mother will let you, I encourage you to accompany her to an appointment so that you can clearly, but gently, inform the provider of this long-standing pattern of behavior. That will help the provider know how to approach her and work with her.
Meanwhile, you have issues of your own that are grounded in an unstable relationship with your mom. You are now almost 30. You are not dependent on her as a mirror for who you are. I hope you will take care of yourself and get the therapy you need to help you claim a personal identity that is more confident.
I wish you well.