You are in a very frustrating position, but I think you answered your own question when you said "I can't help her if she won't let me." It sounds like
you've tried in good faith to offer help, and your mother doesn't want it, for whatever reason, so there is nothing else you can do at the moment. Many adult children face similar frustrations when dealling with elderly parents. It sounds like your mother is struggling to maintain her independance; it's unfortunate that she chooses to do so in a way that is hurtful to you. But you can't force her to do what you think is best for her, and the more you push, the more likely she is to refuse your help.
This doesn't mean you should simply wash your hands of your mother and her problems. I suggest that explain that you want to be there for her, and that the door is open whenever she chooses to accept your help, then back off and stop offering her advice. Keep in touch and visit when you can to make sure she is doing alright. Your mother is at an age when she's at risk for medical problems, so it would be a good idea to contact a couple of her friends or neighbors, and make sure they have your contact information in case they have concerns about your mother's safety, health, or driving abilities.
You might also consider hiring a geriatric care manager in your mother's area. Your mother's behavior could signal some kind of dementia or other mental problem, particularly if it is out of character for her. If she refuses to see a physician, there is little you can do about this, but a geriatric care manager will check in on your mother, and make sure she gets help if she needs it. A geriatric care manager may also be able to help her manage her financial and living situations. Of course, it's possible that your mother won't be any more open to a geriatric care manager than she is to you, but sometimes a non-family member's advice and help is easier to accept.
Finally, you have the right to expect your mother to treat your significant other with respect. Make it clear that you won't stay on the phone with her if she insists on disparaging him, and follow through.
You may find that if you back off a little and stop offering advice, your mother will be more open to you, and some of these power struggles will gradually loose their central place in your relationship.
Good luck, and let us know how it turns out!